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The operation of an optical neural network via a feed-forward (FF) configuration is experimentally simulated in the laboratory. The FF setup is tested using optical injection (OI), and the behavior of follower laser diodes (FLDs) subjected to chaotic modulation is examined. The last two laser diodes (LDs) are exposed to different weights of chaotic modulated signals through optical filtration and attenuation. Observations of the emissions from these two FLDs during FF operation are verified by frequency spectra calculated from time-series data. Signal broadening is assessed by measuring the full width at half maximum (FWHM), and chaotic signal spikes are analyzed by counting the number of peaks associated with signal amplitudes for the FLDs. Additionally, LD control parameters, including the bias voltage of the influencer laser diodes (ILD1, ILD2) and two additional FLDs, are examined. A maximum FWHM of 1.25 GHz for FLD2 is observed with a bias voltage of 3.6 V and a modulated signal attenuation of −12 dB. To determine the synchronization state, the correlation between the ILDs and FLDs is calculated. Results indicate fluctuations between negative and positive values, with the best correlation value being 0.4. These results confirm anti-synchronized ILD-FLDs, which are crucial for ensuring privacy in transmitting units within a chaotic optical communication system simulating an optical neural network. [ABSTRACT FROM AUTHOR]

This paper presents a pioneering approach to bolstering network security and privacy by implementing chaotic optical communication with a hybrid optical feedback system (HOFS). The current baseline methods in network security are often less feasible for hybrid feedback systems, including limited robustness, compromised security, and synchronization challenges. Therefore, this paper proposes a hybrid approach to address these shortcomings by integrating the HOFS into chaotic optical communication systems (HOFS-COCS) to overcome the baseline challenges. This paper aims to improve network security while significantly maintaining efficient communication channels. Moreover, We designed two algorithms, one for chaotic maps generation and another for text encryption and decryption, to improve security in the hybrid feedback system. Our findings demonstrate through rigorous experimentation and analysis that the proposed (HOFS-COCS) method significantly improves network security by enabling reliable chaos generation, synchronization, and secure message transmission in chaotic optical communication systems. This research represents a significant advancement towards enhanced secrecy and synchronization in chaotic optical communication systems, promising a paradigm shift in network security protocols. [ABSTRACT FROM AUTHOR]

In a laser diode (LD) system with optical injection, the effects of gain saturation of the LD on the orbital instability of the system are analyzed numerically. For the optical injection LD system without signal application, it is shown that the effect of optical injection is suppressed in the system with gain saturation and small optical injection, and that a higher amount of optical injection is necessary to obtain similar dynamics. Next, in the optical injection LD system with a pseudo-random signal applied to the LD drive current, it is confirmed that when the dynamics are a periodic window between chaotic and chaotic regions, chaotic dynamics are actualized as the standard deviation of the applied signal becomes larger. Furthermore, it is suggested that this phenomenon can be explained by linear stability analysis, and it is shown by introducing randomly varying tentative gain coefficients that gain fluctuations that lead to an expansion of the chaotic region. Hence, the results of this study provide research on the effects of gain saturation on chaotic oscillation in LDs with pseudo-random signals applied and contribute to the generation of more complex chaotic signals, chaotic secure communication, and random number generation. [ABSTRACT FROM AUTHOR]

This paper explores secure communication systems with a chaotic carrier. The use of chaotic oscillations instead of regular van der Pol oscillators as a signal carrier is a promising and active research area, providing not only communication systems with new protection principles and organization but also high steganographic efficiency when transmitting short messages. The problem is to select methods and techniques for mixing a useful signal into a chaotic one and its recovery on the receiver side, featuring a set of properties acceptable for implementation and real-world application. We demonstrate application of synergetic control theory (SCT), which provides advanced observer-basing methods for nonlinear dynamic systems as well as explore example of data transmission system consisting of a Genesio–Tesi chaotic oscillator, data signal transmission with a method of nonlinear modulation, and recovering with a single-channel synergetic observer at the receiver side. The paper presents a nonlinear state observer modeling procedure followed by building a MATLAB/Simulink simulation model of the data transmission system for the PC-platform along with software implementation for the Raspberry Pi platform, with simulation and experimental run results showing data transmission rates seem to be acceptable for the considered practical applications. Practical applications and limitations issues are discussed. Future research will be universal modeling procedures for different classes of chaotic generators and whole system experimental hardware implementation. The obtained results can be primarily used in short messages and/or encryption keys secure transmission systems, cyber-physical system component command communications, as well as chaotic carrier system R&D competitive studies and other applications. [ABSTRACT FROM AUTHOR]

The utilization of chaotic optical communication, a physical layer security technology, has the potential to enhance the security of optical fiber networks. In this paper, we take knowledge acquired while teaching "A chaotic security system based on phase-intensity (P-I) electro-optic feedback" as an example and, in detail, introduce a teaching implementation process based on the combination of Optisystem and Matlab. Firstly, based on the Lang–Kobayashi (L-K) laser equation, the generation mechanism of electro-optic feedback chaos was explained. Secondly, the P-I electro-optic feedback chaos was analyzed theoretically with the help of Matlab. Finally, a laser chaotic optical communication system based on electro-optic feedback was built with the help of Optisystem (15.0.0) software, and the performance of the communication was simulated and analyzed through the design of system parameters. The teaching design model and facilitate the concretization of the abstract theory of "the principle of chaos generated by electro-optic feedback, the composition of chaotic optical communication system and the performance index of chaotic communication system". Through after-class exercises and questionnaire surveys, it was verified that the teaching method is widely recognized by students and that it effectively improves the teaching effect of the course of laser chaotic communication and the students' academic research ability. [ABSTRACT FROM AUTHOR]

Developing new features for time-series characterization is a current challenge in data science and machine learning. In this paper, we propose a new metric based on a simple and efficient algorithm, namely, the return map. The return map analysis is well established in the field of non-linear dynamics, in particular, for fitting the parameters of a chaotic system from a waveform, or to attack a chaotic communication channel. We show that our metrics work well for both non-linear dynamics and time-series feature extraction problems in the field of machine learning. In an experiment aiming to classify vibration signals of normal and damaged bearings, we compare our method with two other methods that reported to have excellent accuracy, based on entropy and statistical feature distribution, respectively. We show that our method achieves higher accuracy with almost the lowest time costs, which was confirmed in experiments with two different datasets containing three main classes of bearings: normal, with inner race faults, and with outer race faults, having different damage origins and recorded in various conditions. In particular, for the dataset supplied by Case Western Reserve University, our method reached an accuracy of 100% at signals of 5000 sample points length, with a total time of 0.4 s required for feature estimation, while the entropy-based method reached an accuracy of 95% with a time of 100 s, and a statistical feature distribution method reached an accuracy of 93% with a total time of 1.9 s. Results show that the developed method is better suited to real-time bearing condition monitoring applications than most of the methods reported to date. [ABSTRACT FROM AUTHOR]

In the early months of the coronavirus pandemic, Singapore grappled with an escalation of COVID-19 cases among the low-waged foreign workers living in dormitories. Singapore responded to the outbreak by implementing increasingly strict public health measures, which included a partial lockdown and movement restrictions of over 300,000 foreign workers. Our qualitative analysis of the texts created by three key stakeholders (the Singaporean government, local news media, and local non-profit organisations) at the peak of the COVID-19 outbreak in foreign-worker dormitories revealed the construction of contrasting, confusing, and collaborative narratives. These narratives manifested what our paper describes as 'chaotic communication', wherein conflicting and competing messages are crafted or used to build organisation-public or public-public relationships. We also propose 'chaotic narrative spaces' as a conceptual framework to illustrate how social, political, and organisational actors shape narratives about issues and influence the decisions made during a public health crisis. [ABSTRACT FROM AUTHOR]

Chua's circuit is a well-established model for studying chaotic phenomena and is extensively implemented in fields like encrypted communication. However, a traditional Chua's circuit has large volume, high component precision requirements and limited adjustable parameter range, which are not conducive to application. In order to solve these problems, we propose an improved implementation of Chua's circuit on an active inductor and non-autonomous system. First, we adopt the strategy of using active inductors instead of traditional passive inductors, achieving the miniaturization of the circuit and improving the accuracy of inductance. In addition, we present the theory of substituting non-autonomous systems for classical autonomous systems to reduce the requirements for the accuracy of components and improve the robustness of the circuit. Lastly, we connect the extension resistor in parallel with Chua's diode to optimize circuit structure, thereby increasing the range of the adjustable parameter. Based on the three improvements above, experiments have shown that the average maximum error tolerance of components of our improved design has been increased from 1.88% to 7.38% when generating a single vortex, and from 4.73% to 12.61% when generating a double vortex, compared with the traditional Chua's circuit. The range of the adjustable parameter has been increased by 195.83% and 36.98%, respectively, when generating a single vortex and double vortex. In summary, our improved circuit is more practical than the traditional Chua's circuit and has good application value. [ABSTRACT FROM AUTHOR]

This publication investigates the performance of demodulation methods utilized in spread spectrum chaotic communication systems in order to understand conditions at which advanced demodulation methods, such as chaotic synchronization, provide tangible benefits over classical, matched filtering-based approaches. We conduct simulations and comparisons of three different communication systems: classic direct sequence spread spectrum (DSSS), chaotic signal fragment-based pseudo-chaotic spread spectrum (PCSS), and chaotic synchronization-based antipodal chaos shift keying (ACSK). These systems possess similar spectral and time domain characteristics, allowing us to shed light on their fundamental differences and limitations in chaos-based communication. Additionally, we assess the impact of frequency modulation (FM) on these modulation methods, as FM allows the creation of simplified non-coherent modulation schemes. Our findings, based on the analysis of bit error ratio (BER) curves, demonstrate that in the case of a non-dispersive communication channel, the utilization of chaotic synchronization does not allow to achieve performance of correlation-based receivers. Additionally, the utilization of chaotic synchronization for multiple access poses certain challenges due to malicious synchronization between users. As a supplementary finding, we show that in systems with matched filter-based demodulation, discrete-time quantized spreading sequences confer an advantage over analogous, continuous-time spreading waveforms. [ABSTRACT FROM AUTHOR]

This paper proposed a new disturbance observer (DO) based on the fixed-time supper-twisting algorithm (FTSTA) for rejecting perturbations of secure communication of the fractional-order chaotic systems (FOCSs). First, the FOCSs are remodeled into the Takagi–Sugeno fuzzy (TSF) system with the expectation of softening the calculations of the design of the controller and observer. Second, the synchronization control was designed based on the FTSTA sliding mode control (SMC). Third, a new DO for the secure communication system (SCS) of FOCSs was proposed to estimate the disturbance on public channels and uncertainty variations. Fourth, the stability of the proposed synchronization control was obtained by using the Lyapunov condition. Finally, to verify the correction of the proposed method, the MATLAB simulation with the use of FONCOM toolbox was used to meet the desired expectations of theoretically proposed method. There are, small reaching times, small steady-states, and most tested disturbances and parameters' variations were compensated by the proposed DO. [ABSTRACT FROM AUTHOR]

In chaos control, one usually seeks to stabilize the unstable periodic orbits (UPOs) that densely inhabit the attractors of many chaotic dynamical systems. These orbits collectively play a significant role in determining the dynamics and properties of chaotic systems and are said to form the skeleton of the associated attractors. While UPOs are insightful tools for analysis, they are naturally unstable and, as such, are difficult to find and computationally expensive to stabilize. An alternative to using UPOs is to approximate them using cupolets. Cupolets, a name derived from chaotic, unstable, periodic, orbit-lets, are a relatively new class of waveforms that represent highly accurate approximations to the UPOs of chaotic systems, but which are generated via a particular control scheme that applies tiny perturbations along Poincaré sections. Originally discovered in an application of secure chaotic communications, cupolets have since gone on to play pivotal roles in a number of theoretical and practical applications. These developments include using cupolets as wavelets for image compression, targeting in dynamical systems, a chaotic analog to quantum entanglement, an abstract reducibility classification, a basis for audio and video compression, and, most recently, their detection in a chaotic neuron model. This review will detail the historical development of cupolets, how they are generated, and their successful integration into theoretical and computational science and will also identify some unanswered questions and future directions for this work. [ABSTRACT FROM AUTHOR]

Addressing the challenges of high decoding latency, reduced spectral efficiency, and substantial storage requirements in a Cyclic Redundancy Check (CRC)Aided Successive Cancellation List (CA-SCL) polar decoder, this paper proposes a chaotic phase modulation direct-sequence spread spectrum (CPMDSSS)-assisted adaptive serial cancellation list decoding method for underwater acoustic communication. The method involves segmenting the information bits to be transmitted, computing CRC for each segment, and mapping all CRCs to a CPMDSSS, which is then modulated onto the pilot subcarriers of underwater acoustic orthogonal frequency-division multiplexing (OFDM) to increase spectral efficiency. At the receiving end, CRCs are obtained by demodulating the CPMDSSS to verify the segmented information and adaptively select the number of decoding paths. The theoretical analysis and simulation results demonstrate that compared to CA-SCL, the proposed method effectively reduces the required storage units and improves spectral efficiency, with an average reduction of approximately 80% in the decoding paths. Sea trials further indicate that the proposed method reduces the average decoding paths by approximately 71% and decreases the average decoding delay by approximately 64% compared to CA-SCL. [ABSTRACT FROM AUTHOR]

The Internet of Things (IoT) employs various devices with varying hardware capabilities, including those with restricted resources like wireless sensor networks and those with ample resources like satellites. One of the primary hurdles is developing a streamlined encryption algorithm suitable for IoT devices with limited hardware capabilities. This paper introduces an enhanced lightweight algorithm that not only addresses side-channel vulnerabilities but also guards against nonce misuse attacks In this work, we present a design that generates encryption keys using chaotic systems, thereby increasing their unpredictability and randomness. The primary objective of this research is to fortify security measures against a range of novel attack techniques, guaranteeing comprehensive defense, unpredictability, and resilience. The aim of putting strategic defenses and tactics into place is to shield valuable assets from possible threats. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes an image encryption algorithm based on combined 1D chaotic maps. First, a permutation technique was applied. It was then reorganized into 1D matrices along the rows and columns respectively, which were then shuffled by computing the substituted position indices to obtain the scrambled image. Subsequently, a method of confusion of the scrambled image was used through another generated data map, combined with random sub‐matrices for diffusion, then resulting in an encrypted image. Finally, the proposed cryptosystem was implemented in a single kernel platform developed using the Nios II Software Build Tools processor for Eclipse. A hardware architecture was designed using the Qsys‐built tool which is available in the Quartus II 13.0sp1 environment. The developed single‐core system was implemented using the Cyclone IV EP4CE6E22C8. Robustness evaluation of the cryptosystem was performed through security analysis tests such as histogram analysis, correlation coefficient, differential analysis, and key space analysis to prove that it is of good quality, efficient, fast, and successfully resisting brute force attacks. The hardware performance analysis was also carried out. Then the cryptosystem is compared with those in the literature both in the hardware and security performance aspects.

This paper proposes an image encryption algorithm based on combined 1D chaotic maps. First, a permutation technique was applied. It was then reorganized into 1D matrices along the rows and columns respectively, which were then shuffled by computing the substituted position indices to obtain the scrambled image. Subsequently, a method of confusion of the scrambled image was used through another generated data map, combined with random sub‐matrices for diffusion, then resulting in an encrypted image. Finally, the proposed cryptosystem was implemented in a single kernel platform developed using the Nios II Software Build Tools processor for Eclipse. A hardware architecture was designed using the Qsys‐built tool which is available in the Quartus II 13.0sp1 environment. The developed single‐core system was implemented using the Cyclone IV EP4CE6E22C8. Robustness evaluation of the cryptosystem was performed through security analysis tests such as histogram analysis, correlation coefficient, differential analysis, and key space analysis to prove that it is of good quality, efficient, fast, and successfully resisting brute force attacks. The hardware performance analysis was also carried out. Then the cryptosystem is compared with those in the literature both in the hardware and security performance aspects. [ABSTRACT FROM AUTHOR]

We proposed and verified a scheme of chaos synchronization for integrated five-section semiconductor lasers with matching parameters. The simulation results demonstrated that the integrated five-section semiconductor laser could generate a chaotic signal within a large parameter range of the driving currents of five sections. Subsequently, chaos synchronization between two integrated five-section semiconductor lasers with matched parameters was realized by using a common noise signal as a driver. Moreover, it was found that the synchronization was sensitive to the current mismatch in all five sections, indicating that the driving currents of the five sections could be used as keys of chaotic optical communication. Therefore, this synchronization scheme provides a candidate to increase the dimension of key space and enhances the security of the system. [ABSTRACT FROM AUTHOR]

This research article contributes a Chua's diode implementation using a modern active block Current Controlled Current Conveyor Transconductance Amplifier (CCCCTA) with an active MOS transistor for electronically tunable feature. CCCCTA and MOS resistor are responsible for the variation in Chua's diode characteristics and their performance is well studied with the help of dynamical aspects like dissipativity, invariance, bifurcation diagram, Lyapunov exponents, and basin of attraction. The proposed model has a hidden attractor with one unstable node equilibrium and two symmetric stable node equilibrium points. In addition to numerical simulation in MATLAB, the electronic circuit for the proposed Chua's circuit is successfully verified in PSPICE and hardware implementation using commercially available ICs (AD844, CA3080). Chua's traditional chaotic response (double scroll, Rossler, and large limit cycle) can be easily observed by: (i) adjusting the coupling resistor between two capacitor present in a Chua's circuit, (ii) tuning the bias current of CCCCTA present in the proposed Chua's diode, and (iii) by tuning the controlling voltage of MOS resistor (RMOS). The feasibility of the proposed work applies to Chaotic Amplitude Shift Keying (CASK) transmission. Finally, a comparative study is studied with the existing works of literature. [ABSTRACT FROM AUTHOR]

Computer simulation of continuous chaotic systems is usually performed using numerical methods. The discretization may introduce new properties into finite-difference models compared to their continuous prototypes and can therefore lead to new types of dynamical behavior exhibited by discrete chaotic systems. It is known that one can control the dynamics of a discrete system using a special class of integration methods. One of the applications of such a phenomenon is chaos-based communication systems, which have recently attracted attention due to their high covertness and broadband transmission capability. Proper modulation of chaotic carrier signals is one of the key problems in chaos-based communication system design. It is challenging to modulate and demodulate a chaotic signal in the same way as a conventional signal due to its noise-like shape and broadband characteristics. Therefore, the development of new modulation–demodulation techniques is of great interest in the field. One possible approach here is to use adaptive numerical integration, which allows control of the properties of the finite-difference chaotic model. In this study, we describe a novel modulation technique for chaos-based communication systems based on generalized explicit second-order Runge–Kutta methods. We use a specially designed test bench to evaluate the efficiency of the proposed modulation method and compare it with state-of-the-art solutions. Experimental results show that the proposed modulation technique outperforms the conventional parametric modulation method in both coverage and noise immunity. The obtained results can be efficiently applied to the design of advanced chaos-based communication systems as well as being used to improve existing architectures. [ABSTRACT FROM AUTHOR]

In this work, we present a novel four-channel coherent optical chaotic secure communication (COCSC) system, incorporating four simultaneous photonic reservoir computers in tandem with four coherent demodulation units. We employ a quartet of photonic reservoirs that capture the chaotic dynamics of four polarization components (PCs) emitted by a driving QD spin-VCSEL. These reservoirs are realized utilizing four PCs of a corresponding reservoir QD spin-VCSEL. Through these four concurrent photonic reservoir structures, we facilitate high-quality wideband-chaos synchronization across four pairs of PCs. Leveraging wideband chaos synchronization, our COCSC system boasts a substantial 4 × 100 GHz capacity. High-quality synchronization is pivotal for the precise demasking or decoding of four distinct signal types, QPSK, 4QAM, 8QAM and 16QAM, which are concealed within disparate chaotic PCs. After initial demodulation via correlation techniques and subsequent refinement through a variety of digital signal processing methods, we successfully reconstruct four unique baseband signals that conform to the QPSK, 4QAM, 8QAM and 16QAM specifications. Careful examination of the eye diagrams, bit error rates, and temporal trajectories of the coherently demodulated baseband signals indicates that each set of baseband signals is flawlessly retrieved. This is underscored by the pronounced eye openings in the eye diagrams and a negligible bit error rate for each channel of baseband signals. Our results suggest that delay-based optical reservoir computing employing a QD spin-VCSEL is a potent approach for achieving multi-channel coherent optical secure communication with optimal performance and enhanced security. [ABSTRACT FROM AUTHOR]

A short reference differential chaotic shift keying communication system based on reference signal scrambling transformation (RSST-SR-DCSK) is proposed in this paper. The system introduces information-bit-driven scramblers at the transmission end to effectively eliminate the correlation between the reference signal and information signal. At the receiving end, a descrambler is used to restore the correlation, thereby enhancing information transmission security. Additionally, the system employs a short reference transmission mechanism to further increase the information transmission rate. The transmitter and receiver structures of the system are designed through signal structure analysis. Theoretical analyses and simulations conducted in an additive white Gaussian noise (AWGN) channel demonstrate promising performance, including a low bit error rate (BER) and a favorable data-energy-to-bit-energy ratio (DBR). Simulation verification is performed to examine the impact of parameters on the bit error rate performance. A comparative analysis with traditional DCSK and SR-DCSK systems highlights the superior performance of the RSST-SR-DCSK system. [ABSTRACT FROM AUTHOR]

There are several encryption system applications in 5G networks where rapid response is needed, particularly in the military, health sector, traffic, and vehicular movement. This article presents a proposed data security system for 5G networks that fortifies the security of the network through the use of synchronized chaotic systems to produce pseudo-random numbers. The technique by which random numbers are generated during the encryption procedures is closely associated with 5G network security. Many synchronized chaotic systems are used to produce chaotic random models which are used as encryption bases for a wide variety of data. In this study, the encryption was carried out using a variety of data, including two and three-dimensional color images and audio signals of varying lengths, in addition to the use of Fast Fourier Transform (FFT) for encryption of the ingredient energy wave. The results revealed that the algorithm deployed in the process of encryption performed well. Simulations were performed in MATLAB. [ABSTRACT FROM AUTHOR]

This manuscript shows the CMOS design of Lorenz systems using operational transconductance amplifiers (OTAs). Two Lorenz systems are then synchronized in a master–slave topology and used to implement a CMOS secure communication system. The contribution is devoted to the correct design of first- and second-order OTA-C filters, using 180 nm CMOS technology, to guarantee chaotic behavior. First, Simulink is used to simulate a secure communication system using two Lorenz systems connected in a master–slave topology, which is tested using sinusoidal signals that are masked by chaotic signals. Second, the Lorenz systems are scaled to have amplitudes of the state variables below 1 Volt, to allow for CMOS design using OTA-C filters. The transconductances of the OTAs are tuned to accomplish a Laplace transfer function. In this manner, this work highlights the design of a second-order CMOS OTA-C filter, whose damping factor is tuned to generate appropriate chaotic behavior. Finally, chaotic masking is performed by designing a whole CMOS secure communication system by using OTA-C based Lorenz systems, and its SPICE simulation results show its appropriateness for hardware security applications. [ABSTRACT FROM AUTHOR]

Wireless Network security management is difficult because of the ever-increasing number of wireless network malfunctions, vulnerabilities, and assaults. Complex security systems, such as Intrusion Detection Systems (IDS), are essential due to the limitations of simpler security measures, such as cryptography and firewalls. Due to their compact nature and low energy reserves, wireless networks present a significant challenge for security procedures. The features of small cells can cause threats to the network. Network Coding (NC) enabled small cells are vulnerable to various types of attacks. Avoiding attacks and performing secure "peer" to "peer" data transmission is a challenging task in small cells. Due to the low power and memory requirements of the proposed model, it is well suited to use with constrained small cells. An attacker cannot change the contents of data and generate a new Hashed Homomorphic Message Authentication Code (HHMAC) hash between transmissions since the HMAC function is generated using the shared secret. In this research, a chaotic sequence mapping based low overhead 1D Improved Logistic Map is used to secure "peer" to "peer" data transmission model using lightweight H-MAC (1D-LM-P2P-LHHMAC) is proposed with accurate intrusion detection. The proposed model is evaluated with the traditional models by considering various evaluation metrics like Vector Set Generation Accuracy Levels, Key Pair Generation Time Levels, Chaotic Map Accuracy Levels, Intrusion Detection Accuracy Levels, and the results represent that the proposed model performance in chaotic map accuracy level is 98% and intrusion detection is 98.2%. The proposed model is compared with the traditional models and the results represent that the proposed model secure data transmission levels are high. [ABSTRACT FROM AUTHOR]

The purpose of this work is to analyse qualitative features of the information transmission process via several communication schemes based on the synchronization of transmitter and receiver, both being complex signal generators. For this purpose generators of the hyperbolic chaos and generators with the strange nonchaotic attractor are employed. Evaluation of advantages and disadvantages of such schemes is made comparing themselves with each other as well as with schemes based on the nonhyperbolic chaotic generators. Methods. The power spectra and the distributions of the largest finite-time Lyapunov exponent are used to confirm the complexity of the dynamics of the generators in use and to verify the wide-bandness, robustness and stochasticity of their signals. Confidentiality of the informational signal transmission is achieved using its nonlinear mixing to the dynamics of the transmitter. The special phase mixing is used since the model generators employed for the research demonstrate nontrivial dynamics for the angular variable — oscillations phase shift. The digital image is used as an information for transmission. Visual control during the transmission process allows to carry out the qualitative analysis of the success of the signal coding and its detecting by the receiver. Results. Successful transmission and decoding of information for all schemes under investigation are demonstrated for the case of identical transmitter and receiver. Parameter detuning of these generators leads to difficulties in separation of the informational signal from the chaotic/complex carrier due to loss of the full synchronization. For the nonhyperbolic chaos detuning of the parameter responsible for the amplitude of the signal leads to the bad quality of the detection while frequency detuning makes detection absolutely impossible. Schemes with the hyperbolic chaos and strange nonchaotic dynamics appear to demonstrate much better results. The information detection is much better in this case because of the robustness of the generalized synchronization. Conclusion. Robust chaotic and complex nonchaotic generators appear to have significant advantages for communication systems comparing to the chaotic generators of nonhyperbolic type.

The article focuses on the dramatic elements in Raymond Chandler's "The Big Sleep," particularly in chapters 14-16, highlighting their structure as a three-act farce. Topics include the use of Chekhov's gun to advance the plot, the farcical and chaotic nature of the scenes involving multiple guns, and Chandler's commentary on the impact of gun violence in 1930s Los Angeles.

Abstract This paper proposes a multilevel cyclic shift index modulation aided differential chaotic shift keying (MCSI‐DCSK) system to improve data rate and energy efficiency. In the MCSI‐DCSK system, the bit stream is divided into blocks with N(M+1) bits which are further divided into N groups equally. In each group, the first M bits are mapped into an index of cyclic shift in the chaotic reference sequence, while the last bit is used to modulate the shifted chaotic reference sequence. Finally, the all modulated shifted chaotic reference sequences are superimposed to form the information‐bearing signal. So the proposed system improves the data rate. The analytical bit‐error‐rate (BER) expressions of the MCSI‐DCSK system are derived over additive white Gaussian noise and multipath Rayleigh fading channels and validated via simulations. In addition, the BER performance of the proposed system is compared with other non‐coherent, chaotic communication systems. Simulation results indicate that the MCSI‐DCSK system has better performance in data rate and BER.

This paper explores secure communication systems with a chaotic carrier. The use of chaotic oscillations instead of regular van der Pol oscillators as a signal carrier is a promising and active research area, providing not only communication systems with new protection principles and organization but also high steganographic efficiency when transmitting short messages. The problem is to select methods and techniques for mixing a useful signal into a chaotic one and its recovery on the receiver side, featuring a set of properties acceptable for implementation and real-world application. We demonstrate application of synergetic control theory (SCT), which provides advanced observer-basing methods for nonlinear dynamic systems as well as explore example of data transmission system consisting of a Genesio–Tesi chaotic oscillator, data signal transmission with a method of nonlinear modulation, and recovering with a single-channel synergetic observer at the receiver side. The paper presents a nonlinear state observer modeling procedure followed by building a MATLAB/Simulink simulation model of the data transmission system for the PC-platform along with software implementation for the Raspberry Pi platform, with simulation and experimental run results showing data transmission rates seem to be acceptable for the considered practical applications. Practical applications and limitations issues are discussed. Future research will be universal modeling procedures for different classes of chaotic generators and whole system experimental hardware implementation. The obtained results can be primarily used in short messages and/or encryption keys secure transmission systems, cyber-physical system component command communications, as well as chaotic carrier system R&D competitive studies and other applications.

Transformerless grid-connected inverters for photovoltaic (PV) applications provide several advantages such as reduced cost and volume as well as an increased efficiency. However, the removal of the transformer gives rise to several problems related to leakage currents and electromagnetic interferences (EMI). This paper presents different chaotic unipolar sine-pulse width modulation (C-USPWM) techniques for a transformerless grid-connected PV inverter based on parameter selection. The main objective behind this proposed chaotic modulation technique is to reduce the conducted EMI without worsening the power quality and the common-mode voltage (CMV). The method is validated through numerical simulations and experimental tests carried out on laboratory prototype of an optimized H5 inverter (oH5). The obtained results showed its superiority to the conventional unipolar sine-pulse width modulation (USPWM). We showed also that the appropriate parameter selection of the C-UPSWM could advantageously combine an improved EMI performance and an efficient control, making it possible to deliver a significant reduction of the peaks' amplitudes in the frequency spectrum of the common-mode (CM) voltage. [ABSTRACT FROM AUTHOR]

This paper explores the synchronization and implementation of a novel hyperchaotic system using an adaptive observer. Hyperchaotic systems, known for possessing a greater number of positive Lyapunov exponents compared to chaotic systems, present unique challenges and opportunities in control and synchronization. In this study, we introduce a novel hyperchaotic system, thoroughly examining its dynamic properties and conducting a comprehensive phase space analysis. The proposed hyperchaotic system undergoes validation through circuit simulation to confirm its behavior. Introducing an adaptive observer synchronization technique, we successfully synchronize the dynamics of the novel hyperchaotic system with an identical counterpart. Importantly, we extend the application of this synchronization method to the domain of secure communication, showcasing its practical usage. Simulation outcomes validate the effectiveness of our methodology, demonstrating favorable results in the realm of adaptive observer-based synchronization. This research contributes significantly to the understanding and application of hyperchaotic systems, offering insights into both the theoretical aspects and practical implementation. Our findings suggest potential advancements in the field of chaotic systems, particularly in their applications within secure communication systems. By presenting motivations, methods, results, conclusions and the significance of our work in a more appealing manner, we aim to engage readers and highlight the innovative contributions of this study. [ABSTRACT FROM AUTHOR]

This manuscript presents an experimental study of Quadrature Chaos Shift Keying (QCSK) as a means to tighten the physical layer security of Internet of Things (IoT) communication. Our study examines the characteristics and operational aspects of chaos oscillators, prioritizing low-power functionality, resilient chaotic oscillations, and resistance to parameter variations and noise. This study emphasizes the key role of chaos oscillators in enhancing IoT security, showcasing their potential to ensure data integrity. The findings elucidate the dynamics and synchronization stability of the selected oscillators, providing insights into their suitability for secure communication systems. This comprehensive analysis contributes to advancing secure communication methodologies for the expanding landscape of wireless sensor networks in the Internet of Things, underscoring the significance of chaos oscillators in ensuring robust and secure data transmission. [ABSTRACT FROM AUTHOR]

Synchronization of the chaotic systems has attracted much attention in recent years due to its vital applications in secured communication systems. In this paper, an implementation and comparative analysis of two different control approaches for synchronization between two identical four-dimensional hyperchaotic systems is presented. The two control approaches are the Adaptive nonlinear controller and the linear optimal quadratic regulator LQR. To demonstrate the effectiveness of each controller, the numerical simulation is presented using Matlab/Simulink and the control law is derived. The performance of the proposed controllers is compared based on four factors; response time, squared error integration, energy applied from the controller, and cost function. To measure the robustness of the control approaches, the performance factors are compared when there is a change in system parameters and a variation in the initial conditions. Then the proposed synchronization methods are implemented on the FPGA platform to demonstrate the utilized resources on Field Programmable Gate Array (FPGA) hardware platform and the operation speed. Finally, to generalize the results of the comparison, the study is implemented for the synchronization of another secured communication system consisting of two identical three-dimensional chaotic. The experimental results show that the LQR method is more effective than the Adaptive controller based on the performance factors we propose. Moreover, the LQR is much simpler to implement on hardware and requires fewer resources on the FPGA. [ABSTRACT FROM AUTHOR]

The current work is focused on studying the performance of the Pecora–Carroll synchronization technique to achieve synchronization between the analog and discrete chaos oscillators. The importance of this study is supported by the growing applications of chaotic systems for improving the security of data transmission in various communication layers, primarily on the physical layer. The hybrid analog-discrete approach of implementing chaos oscillators opens new possible communication schemes for wireless sensor network (WSN) applications. The analog implementation of chaos oscillators can benefit the simpler sensor node (SN) integration, while the discrete implementation can be used on the gateway. However, the core of such chaos-based communications is synchronizing analog and discrete chaos oscillators. This work studies two key parameters of analog-discrete chaotic synchronization: chaotic synchronization noise immunity and synchronization speed. The noise immunity study demonstrates the quality of synchronization at various noise levels, while the synchronization speed demonstrates how quickly the analog-discrete synchronization is achieved, along with how quickly the two systems diverge when synchronization is no longer present. The two studies use both simulation-based and hardware-based approaches. In the simulation case, the analog oscillator's circuit is modeled in LTspice XVII, while in the hardware case, the circuit is implemented on the PCB. In both simulation and hardware studies, the discrete model of the oscillator is implemented in MATLAB R2023b. The studies are performed for two pairs of different chaos oscillators to widen the proposed approach application potential: the Vilnius and RC chaos oscillators. The oscillators have been selected due to their simplicity and similar dynamic behavior for model-based and electrical circuit implementation. The proposed approach also allows us to compare the synchronization of different oscillators in the analog-discrete implementation. [ABSTRACT FROM AUTHOR]

Various discretization effects caused by applying numerical integration techniques to continuous chaotic systems are broadly studied in nonlinear science. Along with the negative impact on the precision of the various finite-difference schemes, such effects may have surprisingly fruitful practical applications, e.g. pseudo-random number generation, image encryption with improved diffusion and confusion properties, chaotic path planning, and many others. One such application is chaos-based communication systems which gained attention in recent decades due to their high covertness and broadband transmission capability. A crucial problem in the design of chaotic communication systems is the modulation of carrier signals. Due to the noise-like properties of chaotic signals, they can barely be modulated using the same methods as conventional harmonic signals. Thus, developing new modulation techniques is of great interest in the field of chaotic communications. In this study, we investigate the discrete model of the Lorenz oscillator obtained using controllable midpoint numerical integration and develop a novel modulation technique for chaos-based communication systems. We discover and analyze the multistability phenomenon in the dynamics of the investigated finite-difference Lorenz model through bifurcation, the basin of attraction, and Lyapunov spectrum analysis procedures. Using a specially designed testbench, we explicitly show that the proposed modulation method outperforms commonly used parametric modulation and is nearly equal to the state-of-the-art symmetry-based modulation in terms of covertness and noise resistivity. In addition, the proposed modulation technique is much easier to implement using computer arithmetics, especially in fixed-point hardware. The reported results may be efficiently applied to designing advanced chaos-based communications systems or improving the characteristics of existing communication system architectures. [ABSTRACT FROM AUTHOR]

The nonlinear dynamics of nanolasers (NLs), an important component of optical sources, has received much attention. However, there is a lack of in-depth research into the high-quality chaotic output of NLs and their applications in chaotic secure communications. In this paper, we make the NLs generate broadband chaotic signals whose time-delay signatures (TDS) are completely hidden by a phase conjugate feedback structure. And in the two-channel communication scheme, we make the NLs achieve a combination of a low-latency high degree of synchronization and two-channel transmission technique, which enhances the security of message encryption and decryption. We also investigate the effects of system parameters, Purcell factor F , spontaneous emission coupling factor β , and bias current I on the TDS, as well as the effects of parameter mismatch and injection parameters on chaos synchronization and message recovery. The results show that the phase conjugate feedback-based NLs can achieve the suppression of the TDS within a certain parameter range, and it can achieve high-quality synchronization and enhance the security of chaotic communication under appropriate injection conditions. [ABSTRACT FROM AUTHOR]

It is well known that the dynamical characteristics of nano-lasers (NLs) have been extensively studied, but there is limited research on chaotic synchronization communication. In this paper, we propose a closed-loop system of mutually coupled NLs. Firstly, the autocorrelation function is employed to evaluate the capability of the system to conceal the time-delayed signature (TDS), and then, based on this, we specifically analyze the effects of the injection strength, frequency detuning, and parameter mismatch of two NLs on the chaotic synchronization performance, as well as the bidirectional communication. The detailed studies indicate that the proposed closed-loop mutually coupled system based on NLs can achieve high-quality chaotic synchronization with a low TDS and large bandwidth. In addition, the system maintains high-quality chaotic synchronization and communication performance even under significant parameter mismatch. [ABSTRACT FROM AUTHOR]

In this research work, we propose to investigate the effect of fractional-order on the dynamics of a four dimensional (4D) chaotic system by adding a new model of a memristor, which is an essential electronic element with interesting applications. First introduced by Li et al. (Int J Circuit Theory Appl 42(11):1172–1188, 2014, https://doi.org/10.1002/cta.1912), the original system is investigated prior to the more detailed study by Pham et al., The system is found to be self-excited, has a line of equilibrium which are all unstable with regards to the stability condition of fractional-order systems. The bifurcation tools associated with lyapunov exponents reveal the rich dynamics behavior of the proposed system. Our analysis shows that the degree of complexity of the system increases as the fractional-order decreases from 1 to 0.97. Of most/particuar interest, an analog electronic circuit is designed and implemented in PSPICE for verification and confirmed by laboratory experimental measurements. Finally, an ARM-FPGA-based implementation of the 4D fractional-order chaotic system is presented in this work to illustrate the performance of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper proposes a multilevel cyclic shift index modulation aided differential chaotic shift keying (MCSI‐DCSK) system to improve data rate and energy efficiency. In the MCSI‐DCSK system, the bit stream is divided into blocks with N(M+1)$N(M+1)$ bits which are further divided into N groups equally. In each group, the first M bits are mapped into an index of cyclic shift in the chaotic reference sequence, while the last bit is used to modulate the shifted chaotic reference sequence. Finally, the all modulated shifted chaotic reference sequences are superimposed to form the information‐bearing signal. So the proposed system improves the data rate. The analytical bit‐error‐rate (BER) expressions of the MCSI‐DCSK system are derived over additive white Gaussian noise and multipath Rayleigh fading channels and validated via simulations. In addition, the BER performance of the proposed system is compared with other non‐coherent, chaotic communication systems. Simulation results indicate that the MCSI‐DCSK system has better performance in data rate and BER. [ABSTRACT FROM AUTHOR]

It is known, that coherent chaotic communication systems are more vulnerable to noise in the transmission channel than conventional communications. Among the methods of noise impact reduction, such as extended symbol length and various digital filtering algorithms, the optimization of the synchronization coefficient may appear as a very efficient and simple straightforward approach. However, finding the optimal coefficient for the synchronization of two chaotic oscillators is a challenging task due to the high sensitivity of chaos to any disturbances. In this paper, we propose an algorithm for finding the optimal synchronization parameter K_opt for a coherent chaos-based communication system affected by various noises with different signal-to-noise ratios (SNR). It is shown, that under certain conditions, optimal $K$ provides the lowest possible bit error rate (BER) during the transmission. In addition, we show that various metrics applied to the message demodulation task propose different noise immunity to the overall system. For the experimental part of the study, we simulated and physically prototyped two chaotic communication systems based on well-known Rossler and Lorenz chaotic oscillators. The microcontroller-based prototype of a chaotic communication system was developed to investigate the influence of noise in the real transmission channel. The experimental results obtained using the designed hardware testbench are in good correspondence with the theoretical propositions of the study and simulation results. The suggested evaluation metrics and optimization algorithms can be used in the design of advanced chaos-based communication systems with increased performance.

In this paper, a new three-dimensional chaotic system with two exponential nonlinearities is presented. The analysis of fixed points of the proposed system suggests existence of one hyperbolic index-2 spiral saddle-type fixed point. The proposed system fulfils Shilnikov criterion and nature of the chaos is found to be dissipative. Bifurcation diagrams, maximum Lyapunov exponents and Kaplan–Yorke dimension are examined through numerical simulations to investigate dynamics of proposed system. The hardware feasibility of the proposed system is illustrated through current feedback operational amplifier (CFOA)-based circuit implementation. The proposed circuit uses six CFOAs, two diodes to establish nonlinearity, eleven resistors and three capacitors. The absence of analog multiplier in the proposed circuit makes it superior to the existing counterpart in the sense that it does not require area and power-consuming active building block. To confirm the chaotic nature of the proposed circuit, LTspice simulations are done to obtain phase portraits which are found to be strange attractors and are topologically different from the shape of the existing attractors. Moreover, we have investigated the synchronization of the proposed chaotic system using adaptive control scheme and proposed CFOA-based complete circuit design of the adaptively synchronized system. Also, the effect of the tolerance of passive components and temperature on the behavior of the proposed chaotic circuit and the complete synchronization circuit has also been studied. It is found that the circuit is sensitive to the value of resistors and temperature to an extent and can work properly within their limits. [ABSTRACT FROM AUTHOR]

The use of ultra-wideband (UWB) signals for local positioning is very attractive for practice, because such signals have the potential to provide centimeter precision. In this paper, we consider wireless ranging (distance measurement) and positioning, using one of the kinds of UWB signals, i.e., chaotic radio pulses, which are noise-like signals with no constant shape. The distance measurement is based on an assessment in the receiver of the power of UWB chaotic radio pulses emitted by the transmitter. A new method for estimating their power and its experimental implementation is proposed and described. Experimental layouts of the transmitter and receiver and the principles of their operation are described. To determine the main features of this method under real signal propagation conditions, full-scale indoor measurements were carried out, and statistical estimates of the accuracy were made. We present the results of experimental testing of the proposed approach for positioning the emitter relative to a system of anchors in an office space 6 × 6.5 m2 in the mode of measuring object coordinates on a line and on a plane. The mean absolute error (MAE) of distance measurement (1D) was 25 cm, and the root mean squared error (RMSE) was 39 cm. When positioning on a plane (2D), the MAE of coordinate estimation was 34 cm and the RMSE was 42 cm. The proposed distance measurement method is intended for use in wireless UWB transceivers used in wireless sensor networks. [ABSTRACT FROM AUTHOR]

Synchronization capability of two identical chaotic systems can be used for constructing the secure communication systems where the chaotic signal is used as the information carrier. In this paper, a secure communication system is designed by using the bi-directionally synchronized identical Chua's circuits in LC parallel coupling. LC parallel circuit is used as the new coupling element instead of using a single resistor or capacitor or inductor as the coupling element. This makes the complete synchronization of Chua's circuits possible for many different sets of coupling inductance and capacitance values so that the flexibility of constructing the secure communication systems is realized. Both the synchronized Chua's circuits in LC parallel coupling and the corresponding secure communication system are constructed by using the LTspice software. The simulation results show that the secure communication system proposed in the present paper is very efficient for the message transmission for different pairs of coupling inductance and coupling capacitance values where the complete synchronization of Chua's circuits is observed occur. The two essential properties of an ideal secure communication system - perfect message masking and recovery are observed when compared to other secure communication systems already proposed and constructed previously. So, the simulation results of the present study can be used for practically constructing the efficient communication systems in future. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach for secure communication utilizing a chaotic hybrid optical bistable system and chaotic modulation. The proposed crypto system encrypts the message at the transmitter using the chaotic hybrid optical bistable system with decorrelation operation to improve the chaotic sequence's performance. The encoded message is then injected into the dynamics of the chaotic memristor system. At the receiver, the synchronization of the two chaotic systems with passive control and predictive control allows for the recovery of the message through chaotic demodulation. The effectiveness of this approach is demonstrated through numerical simulation using medical images. [ABSTRACT FROM AUTHOR]

It is known, that coherent chaotic communication systems are more vulnerable to noise in the transmission channel than conventional communications. Among the various methods of reducing the noise impact, such as extended symbol length and various digital filtering algorithms, the optimization of the synchronization coefficient may appear as a very efficient and simple straightforward approach. However, finding the optimal coefficient for the synchronization of two chaotic oscillators is a challenging task due to the high sensitivity of chaos to any disturbances. In this paper, we propose an algorithm for finding the optimal synchronization parameter Kopt for a coherent chaos-based communication system affected by various noises with different signal-to-noise ratios (SNR). It is shown, that under certain conditions, optimal K provides the lowest possible bit error rate (BER) during the data transmission. In addition, we show that various metrics applied to the message analysis and demodulation task propose different noise immunity to the overall system. In the experimental part of the study, we simulated and physically prototyped two chaotic communication systems based on well-known Rössler and Lorenz chaotic oscillators. The microcontroller-based prototype of a wire chaotic communication system was developed to investigate the influence of noise in the physical data transmission channel. The experimental results obtained with the designed hardware testbench are in good correspondence with the theoretical propositions of the study and preliminary simulation results. The suggested evaluation metrics and optimization algorithms can be used in the design of advanced chaos-based communication systems with increased performance. [ABSTRACT FROM AUTHOR]

Purpose: With the development of integrated circuit and communication technology, digital secure communication has become a research hotspot. This paper aims to design a five-dimensional fractional-order chaotic secure communication circuit with sliding mode synchronous based on microcontroller (MCU). Design/methodology/approach: First, a five-dimensional fractional-order chaotic system for encryption is constructed. The approximate numerical solution of fractional-order chaotic system is calculated by Adomian decomposition method, and the phase diagram is obtained. Then, combined with the complexity and 0–1 test algorithm, the parameters of fractional-order chaotic system for encryption are selected. In addition, a sliding mode controller based on the new reaching law is constructed, and its stability is proved. The chaotic system can be synchronized in a short time by using sliding mode control synchronization. Findings: The electronic circuit is implemented to verify the feasibility and effectiveness of the designed scheme. Originality/value: It is feasible to realize fractional-order chaotic secure communication using MCU, and further reducing the synchronization error is the focus of future work. [ABSTRACT FROM AUTHOR]

This paper accounts synchronisation of unified chaotic systems using a modified nonlinear active control technique, its circuit analogue circuit implementation, and secure communication. The proposed nonlinear active control approach utilises appropriate states of the unified chaotic systems. The modified nonlinear active control leads to the coupled error dynamics and does not require the external forcing parameters or gains, which differs from the active control techniques reported in the literature. The designed control law ensures the asymptotic stability in large, and the necessary condition is derived using Lyapunov stability theory. Further, the performance of the designed nonlinear active controller is compared based on different time integral performance of the errors with active, adaptive, and sliding mode control techniques. Numerical and circuit simulations are performed in MATLAB and NI-Multisim environments, respectively. Circuit simulated results accord to MATLAB simulation results. Further, unified chaotic system, its synchronisation, and application to secure communication are validated with breadboard circuit/hardware implementation. [ABSTRACT FROM AUTHOR]

This paper presents a new application of the secure communication system (SCS) of the chaotic systems with experimentally verification of wireless devices together with a new stability condition of disturbance observer, which is used to reject the attack signals on public channels and uncertain values on both master and slave of the secure communication system. To ensure the security of the text message transmission, the states of two nonidentical chaotic systems are used to encrypt and decrypt the signal, respectively. To synchronize the slave and master, first, the Lorenz chaotic system is remodeled into the Takagi-Sugeno fuzzy (TSF) model for softening the designs of the controller and observer. Second, to meet the requirement of the sent and received signals are identical, the synchronization controller was designed based on the adaptive sliding mode control (SMC). The adaptive laws of the controller are based on the regulating boundary of saturation thickness. Third, to prevent the attack signals on the public channels and the variations of the system parameters, the disturbance observer (DO) was newly proposed. This is a new contribution of the paper to the area of disturbance observer design. Fourth, the stability of the proposed control method was proved using the Lyapunov condition. Final, the performances of the proposed method are demonstrated via simulation using MATLAB software and experiment using the chips WiFi ESP8266 Shields. The obtained results with attacked signals and parameter' variations were mostly rejected both in simulation and experimental studies. The states of MSSs are identical. Therefore, the sent and received data are completely secured and identical. [ABSTRACT FROM AUTHOR]

Over the past years, many chaos-based secure communication system algorithms have been published for the encryption of different types of data. The problem with these algorithms is either the high complexity that makes them difficult to be implemented or the lack of the high security that prevents them from being applicable in real applications. In this paper, we propose a new highly-secured chaos-based communication system that is based on adaptive control synchronization. The implementation process of the proposed system is detailed including the oscillator dynamic equations, the control laws derivation, the numerical solutions, and the Matlab/Simulink representation. To show the efficiency of the proposed system, its security is analyzed using different security measures. This proofs that the carrier signal is unpredictable by the intruder in both time and frequency domains. The experimental results and the show that the proposed system outperforms the different related and recent work in addition to its stability and robustness to the variation of initial conditions. Finally, we introduce an application on voice encryption to demonstrate the effectiveness of our system. Then We compare the security results of our system with different implementations of recent and related work. [ABSTRACT FROM AUTHOR]

Multistable dynamics analysis of complex chaotic systems is an important problem in the field of chaotic communication security. In this paper, a new hyperchaotic complex Lü system is proposed and its basic dynamics are analyzed. Owing to the introduction of complex variables, the new system has some structurally distinctive attractors, such as flower-shaped and airfoil-shaped attractors. In addition, the evolution process of the limit cycle is also investigated. Next, the multistable coexistence behavior of the system is researched by the method of attraction basins, and the coexistence behavior of two types of hyperchaotic attractors and one type of chaotic and periodic attractors of the system are analyzed. The coexisting hyperchaotic attractors also show flower and airfoil shapes, and four types of coexistence flower-shaped attractors with different structures are perfectly explored. Moreover, the variation of coexistence attractors in the plane and space with parameters is discussed. Then, by introducing a specific piecewise function determined by a two-element method into the new high-dimensional system, the self-reproduction of the attractor can be realized to generate the multistability, and the general steps of attractors self-reproducing in the higher dimensional system are given. Finally, the circuit design of the new system is implemented, which lays a foundation for the application of complex chaotic systems. [ABSTRACT FROM AUTHOR]

We proposed and verified a scheme of chaos synchronization for integrated five-section semiconductor lasers with matching parameters. The simulation results demonstrated that the integrated five-section semiconductor laser could generate a chaotic signal within a large parameter range of the driving currents of five sections. Subsequently, chaos synchronization between two integrated five-section semiconductor lasers with matched parameters was realized by using a common noise signal as a driver. Moreover, it was found that the synchronization was sensitive to the current mismatch in all five sections, indicating that the driving currents of the five sections could be used as keys of chaotic optical communication. Therefore, this synchronization scheme provides a candidate to increase the dimension of key space and enhances the security of the system.

A modulation method is proposed for generating identical UWB chaotic radio pulses using an analog generator of chaotic oscillations. The problem is on the edge of two contradicting requirements: (1) theoretical ability to produce a huge number of various-shape signals, because of high sensitivity to the initial conditions of the generator; (2) the necessity to reproduce oscillations of the same shape both in the receiver and in the transmitter for the implementation of coherent methods of signal processing. The considered method allows us to resolve this contradiction. A single-transistor chaotic oscillator with single power supply and frequency range 100 to 500 MHz is proposed. A mathematical model of the generator (a system of ODEs) was derived. A method of generating chaotic radio pulses with a reproducible shape that could be varied in a manner that is controlled and natural for UWB radio by means of changing the supply voltage of the chaotic oscillator is shown. The mathematical model of the generator is simulated numerically and proves the proposed ideas. The shaping and the replicability of UWB pulses was experimentally proven in an analog domain on a testbed with four instances of the chaotic generator. [ABSTRACT FROM AUTHOR]