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We report the appearance of supertransient chaos in a single and two-coupled Liénard system with the influence of external periodic force. The existence of transient dynamics in a model is significantly long before it settles into the asymptotic steady state of periodic dynamics understood as supertransient chaos. The two diffusively coupled forced Liénard systems exhibit extremely long transient dynamics when their frequencies of the external forcing are slightly mismatched. Additionally, the coupled system signifies supertransient hyperchaotic dynamics for a specific set of system parameters. This study involves different numerical characterizations, statistical analysis, and hardware implementation using an analog electronic circuit. [ABSTRACT FROM AUTHOR]

We present a hyperchaotic oscillator with two linear terms and seven nonlinear terms that displays special algebraic properties. Notably, the introduced oscillator features distinct equilibrium types: single-point, line, and spherical equilibria. The introduced oscillator exhibits attractive dynamics like hyperchaos with two wing attractors. To gain a better understanding, we provide the bifurcation and Lyapunov exponents. The Kolmogorov–Sinai entropy is applied to show the complexity of the oscillator. A microcontroller realization confirms the reliability of the oscillator. The proposed oscillator is successfully applied for RNG. [ABSTRACT FROM AUTHOR]

The design of chaotic systems with complex dynamic behaviors has always been a key aspect of chaos theory in engineering applications. This study introduces a novel fractional-order system characterized by hidden dynamics, hyperchaotic behavior, and multi-scroll attractors. By employing fractional calculus, the system's order is extended beyond integer values, providing a richer dynamic behavior. The system's hidden dynamics are revealed through detailed numerical simulations and theoretical analysis, demonstrating complex attractors and bifurcations. The hyperchaotic nature of the system is verified through Lyapunov exponents and phase portraits, showing multiple positive exponents that indicate a higher degree of unpredictability and complexity. Additionally, the system's multi-scroll attractors are analyzed, showcasing their potential for secure communication and encryption applications. The fractional-order approach enhances the system's flexibility and adaptability, making it suitable for a wide range of practical uses, including secure data transmission, image encryption, and complex signal processing. Finally, based on the proposed fractional-order system, we designed a simple and efficient medical image encryption scheme and analyzed its security performance. Experimental results validate the theoretical findings, confirming the system's robustness and effectiveness in generating complex chaotic behaviors. [ABSTRACT FROM AUTHOR]

Neuromorphic computing draws inspiration from the brain to design energy-efficient hardware for information processing, enabling highly complex tasks. In neuromorphic computing, chaotic phenomena describe the nonlinear interactions and dynamic behaviors. Chaotic behavior can be utilized in neuromorphic computing to accomplish complex information processing tasks; therefore, studying chaos is crucial. Today, more and more color images are appearing online. However, the generation of numerous images has also brought about a series of security issues. Ensuring the security of images is crucial. We propose a novel fourth-direction hyperchaotic system in this paper. In comparison to low-dimensional chaotic systems, the proposed hyperchaotic system exhibits a higher degree of unpredictability and various dynamic behaviors. The dynamic behaviors include fourth-direction hyperchaos, third-direction hyperchaos, and second-direction hyperchaos. The hyperchaotic system generates chaotic sequences. These chaotic sequences are the foundation of the encryption scheme discussed in this paper. Images are altered by employing methods such as row and column scrambling as well as diffusion. These operations will alter both the pixel values and positions. The proposed encryption scheme has been analyzed through security and application scenario analyses. We perform a security analysis to evaluate the robustness and weaknesses of the encryption scheme. Moreover, we conduct an application scenario analysis to help determine the practical usability and effectiveness of the encryption scheme in real-world situations. These analyses demonstrate the efficiency of the encryption scheme. [ABSTRACT FROM AUTHOR]

With the combined call for increased network throughput and security comes the need for high-bandwidth, unconditionally secure systems. Through the combination of true random number generators (TRNGs) for unique seed values, and four-dimensional Lorenz hyperchaotic systems implemented on a Stratix 10 Intel FPGA, we are able to implement 60 MB/s encryption/decryption schemes with 0% data loss on an unconditionally secure system with the NIST standard using less than 400 mW. Further, the TRNG implementation allows for unique encryption outputs for similar images while still enabling proper decryption. Histogram and adjacent pixel analysis on sample images demonstrate that without the key, it is not possible to extract the plain text from the encrypted image. This encryption scheme was implemented via PCIe for testing and analysis. [ABSTRACT FROM AUTHOR]

This paper contributes to the problem of chaos and hyperchaos localization in the fundamental structure of analog building blocks dedicated to single-tone harmonic signal generation. This time, the known Reinartz sinusoidal oscillator is addressed, considering its conventional topology, both via numerical analysis and experiments using a flow-equivalent lumped electronic circuit. It is shown that physically reasonable values of circuit parameters can result in robust dynamical behavior characterized by a pair of positive Lyapunov exponents. Mandatory numerical results prove that discovered strange attractors exhibit all necessary fingerprints of structurally stable chaos. The new "chaotic" parameters are closely related to the standard operation of the investigated analog functional block. A few interestingly shaped, strange attractors have been captured as oscilloscope screenshots. [ABSTRACT FROM AUTHOR]

Recently, the application of memristors in chaotic systems has been extensively studied. Unfortunately, there is limited literature on the introduction of discrete memristors into chaotic maps, especially into non-classical multidimensional maps. For this reason, this paper establishes a new three-dimensional parabolic chaotic map model; in order to improve the complexity and randomness of the map, it is coupled with a square-charge-controlled discrete memristor to design a new four-dimensional memristive hyperchaotic map. Firstly, the stability of the two maps is discussed. And their dynamical properties are compared using Lyapunov exponential spectra and bifurcation diagrams. Then, the phase diagram and iteration sequence of the 4D memristive hyperchaotic map are obtained. Meanwhile, we investigate the hyperchaotic states, the transient chaos, state transfer and attractor coexistence phenomena of the four-dimensional memristive map. In particular, the special state transfer phenomenon of switching from a periodic attractor to a quasi-periodic attractor and the special coexistence phenomenon of a quasi-periodic attractor coexisting with a quasi-periodic attractor around fixed points are found, which have not been observed in other systems. Finally, the phase-track diagrams and iterative sequence diagrams of the four-dimensional memristive map are verified on a digital experimental platform, revealing its potential for practical applications. [ABSTRACT FROM AUTHOR]

With the advancement in information and communication technologies (ICTs), the widespread dissemination and sharing of digital images has raised concerns regarding privacy and security. Traditional methods of encrypting images often suffer from limitations such as a small key space and vulnerability to brute-force attacks. To address these issues, this paper proposes a novel eighth-order hyperchaotic system. This hyperchaotic system exhibits various dynamic behaviors, including hyperchaos, sub-hyperchaos, and chaos. The encryption scheme based on this system offers a key space larger than 22338. Through a comprehensive analysis involving histogram analysis, key space analysis, correlation analysis, entropy analysis, key sensitivity analysis, differential attack analysis, and cropping attack analysis, it is demonstrated that the proposed system is capable of resisting statistical attacks, brute force attacks, differential attacks, and cropping attacks, thereby providing excellent security performance. [ABSTRACT FROM AUTHOR]

Forecasting the dynamical behaviors of nonlinear systems over long time intervals represents a great challenge for scientists and has become a very active area of research. The employment of the well-known artificial recurrent neural networks (RNNs)-based models requires a high computational cost, and they usually maintain adequate accuracy for complicated dynamics over short intervals only. In this work, an efficient reservoir-computing (RC) approach is presented to predict the time evolution of the complicated dynamics of a fractional order hyperchaotic finance model. Compared with the well-known deep learning techniques, the suggested RC-based forecasting model is faster, more accurate for long-time prediction, and has a smaller execution time. Numerical schemes for fractional order systems are generally time-consuming. The second goal of the present study is to introduce a faster, more efficient, and simpler simulator to the fractional order chaotic/hyperchaotic systems. The RC model is utilized in a proposed RC-based digital image encryption scheme. Security analysis is carried out to verify the performance of the proposed encryption scheme against different types of statistical, KPA, brute-force, CCA, and differential attacks. [ABSTRACT FROM AUTHOR]

Weakly coupled semiconductor superlattices under DC voltage bias are nonlinear systems with many degrees of freedom whose nonlinearity is due to sequential tunneling of electrons. They may exhibit spontaneous chaos at room temperature and act as fast physical random number generator devices. Here we present a general sequential transport model with different voltage drops at quantum wells and barriers that includes noise and fluctuations due to the superlattice epitaxial growth. Excitability and oscillations of the current in superlattices with identical periods are due to nucleation and motion of charge dipole waves that form at the emitter contact when the current drops below a critical value. Insertion of wider wells increases superlattice excitability by allowing wave nucleation at the modified wells and more complex dynamics. Then hyperchaos and different types of intermittent chaos are possible on extended DC voltage ranges. Intrinsic shot and thermal noises and external noises produce minor effects on chaotic attractors. However, random disorder due to growth fluctuations may suppress any regular or chaotic current oscillations. Numerical simulations show that more than 70% of samples remain chaotic when the standard deviation of their fluctuations due to epitaxial growth is below 0.024 nm (10% of a single monolayer) whereas for 0.015 nm disorder suppresses chaos. [ABSTRACT FROM AUTHOR]

This paper strives to achieve a comprehensive review of chaos in analog circuits and lumped electronic networks. Readers will be guided from the beginning of the investigations of simple electronic circuits to the current trends in the research into chaos. The author tries to provide the key references related to this issue, including papers describing modern numerical algorithms capable of localizing chaotic and hyperchaotic motion in complex mathematical models, interesting full on-chip implementations of chaotic systems, possible practical applications of entropic signals, fractional-order chaotic systems and chaotic oscillators with mem-elements. [ABSTRACT FROM AUTHOR]

The main goal of this work is to optimize the chaotic behavior of a three-dimensional chaotic-spherical-attractor-generating fractional-order system and compare the results with its novel hyperchaotic counterpart. The fractional-order chaotic system is a smooth system perturbed with a hyperbolic tangent function. There are two major contributions in this investigation. First, the maximum Lyapunov exponent of the chaotic system was optimized by applying evolutionary algorithms, which are meta-heuristics search algorithms, namely, the differential evolution, particle swarm optimization, and invasive weed optimization. Each of the algorithms was populated with one hundred individuals, the maximum generation was five hundred, and the total number of design variables was eleven. The results show a massive increase of over 5000% in the value of the maximum Lyapunov exponent, thereby leading to an increase in the chaotic behavior of the system. Second, a hyperchaotic system of four dimensions was constructed from the inital chaotic system. The dynamics of the optimized chaotic and the new hyperchaotic systems were analyzed using phase portraits, time series, bifurcation diagrams, and Lyapunov exponent spectra. Finally, comparison between the optimized chaotic systems and the hyperchaotic states shows an evidence of more complexity, ergodicity, internal randomness, and unpredictability in the optimized systems than its hyperchaotic counterpart according to the analysis of their information entropies and prediction times. [ABSTRACT FROM AUTHOR]

This paper describes recent findings achieved during a numerical investigation of the circuit known as the Clapp oscillator. By considering the generalized bipolar transistor as an active element and after applying the search-for-chaos optimization approach, parameter regions that lead to either chaotic or hyperchaotic dynamics were discovered. For starters, the two-port that represents the transistor was firstly assumed to have a polynomial-forward trans-conductance; then the shape of trans-conductance changes into the piecewise-linear characteristics. Both cases cause vector field symmetry and allow the coexistence of several different attractors. Chaotic and hyperchaotic behavior were deeply analyzed by using standard numerical tools such as Lyapunov exponents, basins of attraction, bifurcation diagrams, and solution sensitivity. The structural stability of strange attractors observed numerically was finally proved via a real practical experiment: a flow-equivalent chaotic oscillator was constructed as the lumped electronic circuit, and desired attractors were captured and provided as oscilloscope screenshots. [ABSTRACT FROM AUTHOR]

Considering a nonlinear dynamic oscillator, a high Lyapunov exponent indicates a high degree of randomness useful in many applications, including cryptography. Most existing oscillators yield very low Lyapunov exponents. The proposed work presents a general strategy to derive an n-D hyperchaotic map with a high Lyapunov exponent. A 2D case study was analyzed using some well-known nonlinear dynamic metrics including phase portraits, bifurcation diagrams, finite time Lyapunov exponents, and dimension. These metrics indicated that the state of the novel map was more scattered in the phase plane than in the case of some traditional maps. Consequently, the novel map could produce output sequences with a high degree of randomness. Another important observation was that the first and second Lyapunov exponents of the proposed 2D map were both positive for the whole parameter space. Consequently, the attractors of the map could be classified as hyperchaotic attractors. Finally, these hyperchaotic sequences were exploited for image encryption/decryption. Various validation metrics were exploited to illustrate the security of the presented methodology against cryptanalysts. Comparative analysis indicated the superiority of the proposed encryption/decryption protocol over some recent state-of-the-art methods. [ABSTRACT FROM AUTHOR]

In this work, a 4D hyperchaotic hyperjerk system, with better results for its Lyapunov exponents and Kaplan-Yorke dimension regarding other systems of this family, as well as its circuit implementation, is presented. Hyperchaotic hyperjerk systems depict complex dynamical behavior in a high-dimensional phase space with n ≥ 4, offering robustness against many types of attacks in private communications. For this reason, an adaptive controller in order to achieve global chaos synchronization of coupled 4D hyperchaotic hyperjerk systems with unknown parameters is designed. The adaptive results in this work are proved using Lyapunov stability theory and the effectiveness of the proposed synchronization scheme is confirmed through the simulation results. [ABSTRACT FROM AUTHOR]

This paper introduces a new memristor-based hyperchaotic complex Lü system (MHCLS) and investigates its adaptive complex generalized synchronization (ACGS). Firstly, the complex system is constructed based on a memristor-based hyperchaotic real Lü system, and its properties are analyzed theoretically. Secondly, its dynamical behaviors, including hyperchaos, chaos, transient phenomena, as well as periodic behaviors, are explored numerically by means of bifurcation diagrams, Lyapunov exponents, phase portraits, and time history diagrams. Thirdly, an adaptive controller and a parameter estimator are proposed to realize complex generalized synchronization and parameter identification of two identical MHCLSs with unknown parameters based on Lyapunov stability theory. Finally, the numerical simulation results of ACGS and its applications to secure communication are presented to verify the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes a new four-dimensional hyperchaotic map based on the Rabinovich system to realize chaotic encryption in higher dimension and improve the security. The chaotic sequences generated by Runge-Kutta method are combined with the chaotic sequences generated by an exponential chaos map to generate key sequences. The key sequences are used for image encryption. The security test results indicate that the new hyperchaotic system has high security and complexity. The comparison between the new hyperchaotic system and the several low-dimensional chaotic systems shows that the proposed system performs more efficiently. [ABSTRACT FROM AUTHOR]

We study the chaos and hyperchaos of Rydberg-dressed Bose–Einstein condensates (BECs) in a one-dimensional optical lattice. Due to the long-range, soft-core interaction between the dressed atoms, the dynamics of the BECs are described by the extended Bose-Hubbard model. In the mean-field regime, we analyze the dynamical stability of the BEC by focusing on the ground state and localized state configurations. Lyapunov exponents of the two configurations are calculated by varying the soft-core interaction strength, potential bias, and length of the lattice. Both configurations can have multiple positive Lyapunov exponents, exhibiting hyperchaotic dynamics. We show the dependence of the number of the positive Lyapunov exponents and the largest Lyapunov exponent on the length of the optical lattice. The largest Lyapunov exponent is directly proportional to areas of phase space encompassed by the associated Poincaré sections. We demonstrate that linear and hysteresis quenches of the lattice potential and the dressed interaction lead to distinct dynamics due to the chaos and hyperchaos. Our work is relevant to current research on chaos as well as collective and emergent nonlinear dynamics of BECs with long-range interactions. [ABSTRACT FROM AUTHOR]

Trigonometric functions were used to construct a 2-D symmetrical hyperchaotic map with infinitely many attractors. The regime of multistability depends on the periodicity of the trigonometric function, which is closely related to the initial condition. For this trigonometric nonlinearity and the introduction of an offset controller, the initial condition triggers a specific multistability evolvement, in which infinitely countless symmetric and asymmetric attractors are produced. Initial condition-triggered offset boosting is explored, combined with constant controlled offset regulation. Furthermore, this symmetric map gives the sequences in various types of asymmetric attractors, in which the polarity balance is maintained by the initial condition and a negative coefficient due to the trigonometric function. Finally, as determined through the hardware implementation of STM32, the corresponding results agree with the numerical simulation. [ABSTRACT FROM AUTHOR]

The protection of video data has become a hot topic of research. Researchers have proposed a series of coding algorithms to ensure the safe and efficient transmission of video information. We propose an encryption scheme that can protect video information with higher security by combining the video coding algorithm with encryption algorithm. The H.264/AVC encoding algorithm encodes the video into multiple slices, and the slices are independent of each other. With this feature, we encrypt each slice while using the cipher feedback (CFB) mode of the advanced encryption standard (AES) with the dynamic key. The key is generated by the pseudo-random number generator (PRNG) and updated in real time. The encryption scheme goes through three phases: constructing plaintext, encrypting plaintext, and replacing the original bitstream. In our scheme, we encrypt the code stream after encoding, so it does not affect the coding efficiency. The purpose of the CFB mode while using the AES encryption algorithm is to maintain the exact same bit rate and produce a format compatible bitstream. This paper proposes a new four-dimensional (4-D) hyperchaotic algorithm to protect data privacy in order to further improve the security of video encryption. Symmetric encryption requires that the same key is used for encryption and decoding. In this paper, the symmetry method is used to protect the privacy of video data due to the large amount of video encrypted data. In the experiment, we evaluated the proposed algorithm while using different reference video sequences containing motion, texture, and objects. [ABSTRACT FROM AUTHOR]