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Chua's circuit represents a paradigm for nonlinear dynamics and chaos in electronic circuits. In this paper, its discrete-time counterpart is considered showing the occurrence of nonlinear resonance when driven by an external sinusoidal input. Evidences of jump resonance are revealed from several regions of the parameter space. An approach based on quasi-analytic methods, numerical simulations and several experiments with digital microprocessors is presented, further confirming the richness of Chua's circuit dynamical behavior. The high selectivity of the jump resonance observed from the discrete-time Chua's circuit paves the way for the implementation of low-cost high-resolution frequency drift sensing devices. [ABSTRACT FROM AUTHOR]

This paper introduces a novel node centrality index based on edge dynamics in a complex network: adjacent edge index. Through the analysis of network dynamics and topology, we provide a neat index to qualify node importance, which is calculated by the eigenvector components corresponding to the Fiedler value of the network. Notably, it identifies nodes whose adjacent edge sets play a significant role in network synchronization. The index indicates that not only a node's degree but also its location should be considered. To demonstrate the effectiveness of the proposed index, consider a double-star network and a Jazz Musicians network in which chaotic Chua's circuits as nodes are coupled. By factoring in the dynamic information exchange between nodes and their neighbors, this index offers valuable insights for optimizing strategies in engineering areas such as efficient information dissemination. [ABSTRACT FROM AUTHOR]

In this paper, a grounded meminductor emulator has been proposed using six MOSFETs (3NMOS and 3PMOS) only. Three transconductance stages and two capacitors are generally required to realize a meminductor emulator. Meminductor is considered as an inductor having memory. In the proposed design of meminductor emulator, the gyrator circuit is realized using common-source and common-gate amplifiers with one capacitor. The first capacitor is used to obtain the behaviour of inductance while the second capacitor is used for charge storage which acts as a memory element. In the proposed design of meminductor emulator, the gate-to-source capacitor of MOSFET is utilized in place of external capacitor for memory element. Therefore, the proposed design is free from the requirement of passive components as the required capacitor is formed by MOSFET. Also, the frequency characteristics of proposed meminductor are found to be satisfactory up to 100 MHz. The other essential characteristics such as non-volatility test, temperature analysis, tunability, Monte Carlo, and corner analysis are also found to be satisfactory. The proposed design of meminductor emulator is compared with other existing meminductor emulators. The performance of the emulator is successfully verified through the realization of chaotic oscillator circuit. [ABSTRACT FROM AUTHOR]

This paper introduces a floating flux-controlled meminductor emulator, implemented using two voltage differencing differential difference amplifier (VDDDA) along with a memristor and capacitor. Grounded and floating configurations are simulated with TSMC 0.18 µm level-49 BSIM3 CMOS process parameters in LTspice, showcasing the performance of the proposed circuits. The circuit features electronic tunability, allowing for the adjustment of nonlinear flux through the tuning of bias voltage. Simulation results validate the frequency-dependent current-flux dynamics of the proposed meminductor emulator. The simulation results, which involve frequency-dependent pinched hysteresis loops, transient analysis, non-volatility, and Monte Carlo analysis of the proposed meminductor, affirm the functionality and adequacy of the proposed design. A Chua’s oscillator is realized using proposed VDDDA-based meminductor as non-linear element.

The onset of jump resonance in the driven Chua's circuit is deeply described in this paper, further confirming the role of Chua's circuit in nonlinear circuits and systems theory. The study of the conditions under which this peculiar behavior occurs is based on the possibility of obtaining a Lur'e representation of the driven Chua's circuit and applying the describing function approach. Design considerations to select the Chua's circuit parameters in order to shape the jump resonance features are given, providing the nonlinear core for highly selective frequency drift sensors. [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]

It becomes crucial to calculate the Hamilton energy and its evolution when exploring dynamics characters in nonlinear systems. Based on the Helmholtz's theorem, the Hamilton energy of the HR system in an electric field and the modified Chua's circuit are calculated and analyzed. Then the energy feedback is used to control the system to the desired states. The results show that this method can not only effectively suppress the chaotic behavior of the system, but also induce abundant discharge behavior. In addition, the synchronization behavior of the two HR systems or Chua's circuits is explored respectively using the adaptive synchronization control method. Taking into account that different Lyapunov functions will yield different results, we propose the idea that the coefficient ratio of each state variable in the Hamilton energy function can be utilized to design the Lyapunov function for the dynamic systems in this paper. It is found that the controller and parameter adaptive law obtained by this method can make the drive system and response system realize quasi-synchronization. This result provides an effective method for further exploring adaptive synchronization between neurons. [ABSTRACT FROM AUTHOR]

This paper investigates the event-triggered impulsive synchronization of a variable-order fractional chaotic Lur'e system with the application of fractal interpolation based image encryption. The variable-order fractional Lur'e system is modeled into fractional order Chua's circuit model with short memory. The synchronization is achieved using event-triggered impulsive control and short memory for chaotic Lur'e systems, employing linear matrix inequalities. The variable-order fractional Chua's circuit systems successfully accomplish their synchronization using both impulsive and event-triggered impulsive control. Furthermore, fractal interpolation function (with function scalings) is applied to reconstruct the chaotic attractors. The Riemann-Liouville variable-order fractional calculus of diverse fractal functions is also investigated in connection with the study on variable-order fractional systems. The interpolated sequence, along with the Arnold transform, modified Fisher Yates algorithm, and additive diffusion, is utilized to propose an image encryption algorithm. Various statistical analyses are conducted to assess the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper introduces a floating flux-controlled meminductor emulator, implemented using two voltage differencing differential difference amplifier (VDDDA) along with a memristor and capacitor. Grounded and floating configurations are simulated with TSMC 0.18 µm level-49 BSIM3 CMOS process parameters in LTspice, showcasing the performance of the proposed circuits. The circuit features electronic tunability, allowing for the adjustment of nonlinear flux through the tuning of bias voltage. Simulation results validate the frequency-dependent current-flux dynamics of the proposed meminductor emulator. The simulation results, which involve frequencydependent pinched hysteresis loops, transient analysis, non-volatility, and Monte Carlo analysis of the proposed meminductor, affirm the functionality and adequacy of the proposed design. A Chua's oscillator is realized using proposed VDDDA-based meminductor as non-linear element. [ABSTRACT FROM AUTHOR]

This paper delves into the topics of Finite-Time Stabilization (FTS) and Finite-Time Contractive Stabilization (FTCS) for Fractional-Order Nonlinear Systems (FONSs). To address these issues, we employ a State-Dependent Delayed Impulsive Controller (SDDIC). By leveraging both Lyapunov theory and impulsive control theory, we establish sufficient conditions for achieving stability criteria for fractional-order systems. Initially, we employ the aforementioned sufficient conditions to derive stability criteria for general FONSs within the SDDIC framework, employing Linear Matrix Inequality (LMI) techniques. Furthermore, we apply these theoretical findings to tackle the challenge of finite-time synchronization in fractional-order chaotic systems using the proposed SDDIC. We substantiate the efficacy of these theoretical advancements through numerical simulations that vividly demonstrate their capability to achieve finite-time synchronization in fractional-order cellular neural networks and fractional-order Chua's circuits. Moreover, we introduce an innovative chaos-based multi-image encryption algorithm, thereby contributing significantly to the field. To ensure the algorithm's robustness, we subject it to rigorous statistical tests, which confidently affirm its capacity to provide the requisite level of security. [ABSTRACT FROM AUTHOR]

In this paper, we present a fully integrated circuit without inductance implementing Chua's chaotic system. The circuit described in this study utilizes the SMIC 180 nm CMOS process and incorporates a multi-path voltage-controlled oscillator (VCO). The integral-differential nonlinear resistance is utilized as a variable impedance component in the circuit, constructed using discrete devices from a microelectronics standpoint. Meanwhile, the utilization of a multi-path voltage-controlled oscillator ensures the provision of an adequate oscillation frequency and a stable waveform for the chaotic circuit. The analysis focuses on the intricate and dynamic behaviors exhibited by the chaotic microelectronic circuit. The experimental findings indicate that the oscillation frequency of the VCO can be adjusted within a range of 198 MHz to 320 MHz by manipulating the applied voltage from 0 V to 1.8 V. The circuit operates within a 1.8 V environment, and exhibits power consumption, gain–bandwidth product (GBW), area, and Lyapunov exponent values of 1.0782 mW, 4.43 GHz, 0.0165 mm2, and 0.6435∼1.0012, respectively. The aforementioned circuit design demonstrates the ability to generate chaotic behavior while also possessing the benefits of low power consumption, high frequency, and a compact size. [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.

Amnesia-resistive chaotic circuits have various application prospects due to their unique circuit characteristics. In this paper, by studying the relationship between memristors and chaotic circuits, two models of magneto-controlled memristors with smooth quadratic monotonic rise nonlinear characteristics are constructed based on Tsai’s circuit, and an active memristor circuit composed of negative conductance is combined to replace Tsai’s diode in Tsai’s circuit system, and then a magneto-controlled memristor is inserted between the LC resonant part of the circuit, thus establishing a heterogeneous memristor second-order chaotic circuit. Multisim is used for device modeling, circuit construction, and system composition and simulation. The simulation tests show that when t ∈ [0,900] ∪ [1800,2500], the system exhibits a chaotic state. When t ∈ (900,1800), the system exhibits a periodic state. As the initial value parameter d varies between [2,4.64], the state of the system shifts between chaotic and hyperchaotic states, while the complexity of the system changes back and forth. This study demonstrates that the heterogeneous magneto-controlled memristor chaotic circuit has a rich, chaotic behavior, providing an effective reference for applying chaotic memristor circuits.

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 focuses on the synchronization control problem for neural networks (NNs) subject to stochastic cyber-attacks. Firstly, an adaptive event-triggered scheme (AETS) is adopted to improve the utilization rate of network resources, and an output feedback controller is constructed for improving the performance of the system subject to the conventional deception attack and accumulated dynamic cyber-attack. Secondly, the synchronization problem of master–slave NNs is transformed into the stability analysis problem of the synchronization error system. Thirdly, by constructing a customized Lyapunov–Krasovskii functional (LKF), the adaptive event-triggered output feedback controller is designed to ensure the synchronization error system is asymptotically stable with a given H ∞ performance index. Lastly, in the simulation part, two examples, including Chua's circuit, illustrate the feasibility and universality of the related technologies in this paper. [ABSTRACT FROM AUTHOR]

In this paper, a modified hyperchaotic memristor-based Chua's circuit and its generalized discrete model are reported. First, the dynamics of the continuous system are investigated using different tools, including stability theory, phase portraits, Lyapunov exponents, and bifurcation diagrams, showing that the proposed circuit model possesses a line of equilibrium and exhibits rich dynamics, including the coexistence of regular and chaotic attractors, and mixed-mode oscillations. Lastly, a generalized discrete version of the proposed system is formulated and its dynamics are explored. Using the Jury criterion, we constructed a useful stability test to localize some stable regions in three parameter planes. The presence of an exact periodic solution is numerically highlighted, and the occurrence of chaotic behavior is confirmed using the largest Lyapunov exponent and the 0−1 test. [ABSTRACT FROM AUTHOR]

Abstract Chaos is a deterministic phenomenon that occurs in a non-linear dynamic system under specific condition when the trajectories of the state vector become periodic and extremely sensitive to the initial conditions. While traditional resistor-based chaotic communications are primarily concerned with the safe transfer of information across networks, the transceivers themselves can be compromised due to outsource manufacturing. With the growth of wireless sensors in resource-constrained implantable and wearable devices, chaotic communication may be a good fit if the information transmitted is reliable and the transmitter devices are secure. We believe that memristor, as the fourth fundamental two-terminal circuit element, can close the gap between reliable communication and secure manufacturing since its resistance can be programmed and saved by the designer and not the foundry. Thus, in this paper, we propose a memristor-based Chua’s chaotic transceiver that is both reliable in the presence of eavesdroppers and secure against untrusted foundries. Specifically, we consider the pair of transmitter and receiver under the same memristor value to show the possibility of uninterrupted communication as well as cases where different values of memristors are used to find out the possible range in which the message can still be meaningfully decoded. Experimental results confirm that both reliable communication and secure design can be achieved via our proposed memristor-based chaos transceivers.

In this paper, we present a fully integrated circuit without inductance implementing Chua’s chaotic system. The circuit described in this study utilizes the SMIC 180 nm CMOS process and incorporates a multi-path voltage-controlled oscillator (VCO). The integral-differential nonlinear resistance is utilized as a variable impedance component in the circuit, constructed using discrete devices from a microelectronics standpoint. Meanwhile, the utilization of a multi-path voltage-controlled oscillator ensures the provision of an adequate oscillation frequency and a stable waveform for the chaotic circuit. The analysis focuses on the intricate and dynamic behaviors exhibited by the chaotic microelectronic circuit. The experimental findings indicate that the oscillation frequency of the VCO can be adjusted within a range of 198 MHz to 320 MHz by manipulating the applied voltage from 0 V to 1.8 V. The circuit operates within a 1.8 V environment, and exhibits power consumption, gain–bandwidth product (GBW), area, and Lyapunov exponent values of 1.0782 mW, 4.43 GHz, 0.0165 mm2, and 0.6435∼1.0012, respectively. The aforementioned circuit design demonstrates the ability to generate chaotic behavior while also possessing the benefits of low power consumption, high frequency, and a compact size.

Abstract The article shows that transient chaos phenomena can be observed in a generalized memristor Chua's circuit where a nonlinear resistor is introduced to better model the real memristor behaviour. The flux‐charge analysis method is used to explain the origin of transient chaos, that is attributed to the drift of the index of the memristor circuit invariant manifolds caused by the charge flowing into the nonlinear resistor.

Chaos phenomenon is a unique behavior of nonlinear dynamical systems ubiquitous in nature, which is unpredictable and sensitive to initial conditions. Chaos synchronization was widely used in biology, medicine, secure communication and so on. A fourdimensional dynamic system was established by parallel Josephson junction on the basis of Chua's circuit, and its dynamic behavior was analyzed. The results show that the circuit can exhibit periodic and chaotic states. Secondly, combined with numerical simulation, the complete synchronization behavior of capacitor coupling two periodic systems, two chaotic systems or periodic and chaotic system was clussfied and discussed. The results show that the complete synchronization can be achieved by changing the coupling strength of two completely identical periodic systems or two completely identical chaotic systems, regardless of whether there is an external magnetic field. However, the coupling system with two different parameters cannot achieve perfect synchronization, but under the appropriate external magnetic field, almost complete synchronization can be achieved. [ABSTRACT FROM AUTHOR]

Oscillatory circuits with real memristors have attracted a lot of interest in recent years. The vast majority of circuits involve volatile memristors, while less explored is the use of non-volatile ones. This paper considers a circuit composed by the interconnection of a two-terminal (one port) element, based on the linear part of Chua’s circuit, and a non-volatile memristor obeying the Stanford model. A peculiar feature of such a memristor is that its state displays negligible time-variations under some voltage threshold. Exploiting this feature, the memristor is modeled below threshold as a programmable nonlinear resistor whose resistance depends on the gap distance. Then, the first-order Harmonic Balance (HB) method is employed to derive a procedure to select the parameters of the two-terminal element in order to generate programmable subthreshold oscillatory behaviors, within a given range of the gap, via a supercritical Hopf bifurcation. Finally, the dynamic behaviors of the designed circuits as well as the sensitivity of the procedure with respect to the location of the bifurcating equilibrium point and the range of the gap are discussed and illustrated via some application examples.

This paper deals with generalised Caputo fractional proportional linear time-invariant systems in a finite-dimensional space. The Laplace transformation method ensures the analytical solution of the desired fractional linear time-invariant systems. The present article presents the necessary and sufficient conditions for controllability and observability of the generalised Caputo proportional fractional linear time-invariant systems. These two properties can play a more fundamental role in system analysis before controller and observer designs are engaged. Moreover, we have acquired the criterion for generalised Caputo proportional fractional linear time-invariant systems as Kalman rank conditions. Some numerical examples are presented to show the applicability of the paper to demonstrate our findings. Finally, we derive the necessary and sufficient controllability conditions for the generalised Caputo proportional fractional-order nonlinear Chua's electric circuit. [ABSTRACT FROM AUTHOR]

The development by Hewlett-Packard of memristor, a fourth fundamental electronic component, has gained attention in the fields of memory technology and neuromorphic. As memristor components are not currently available commercially, modelling of memristors with associated circuit elements is required to build application circuits. In this work, based on the Hewlett-Packard memristor, we implement a new Chua's chaotic circuit, which is a simple combination of electronic components which exhibit chaos. The nonlinear element in Chua's circuit is substituted with an active memristor-based circuit consisting of a combination of negative resistor and TiO2-based memristor, which allows the circuit to exhibit chaos without scaling the differential equations and produces realistic voltages and currents across the circuit components. This paper indicates for the first time, chaotic oscillations are produced using memristor-based Chua's circuit where actual physical equations, describing the memristor, are applied. The analysis of the proposed single memristor-based chaotic is discussed. Such a circuit is of interest in chaos-based systems for applications such as wireless communication. [ABSTRACT FROM AUTHOR]

Since the invention of Chua's circuit, numerous generalizations based on the substitution of the nonlinear function have been reported. One of the generalizations is obtained by substituting cubic nonlinearity for piece-wise linear (PWL) nonlinearity. Although hidden chaotic attractors with a PWL nonlinearity have been discovered in the classical Chua's circuit, chaotic attractors with a smooth cubic nonlinearity have long been known as self-excited attractors. Through a systematically exhaustive computer search, this paper identifies coexisting hidden attractors in the smooth cubic Chua's circuit. Either self-excited or coexisting hidden attractors are now possible in the smooth cubic Chua's circuit with algebraically elegant values of both initial points and system parameters. The newly found coexisting attractors exhibit an inversion symmetry. Both initial points and system parameters are equally required to localize hidden attractors. Basins of attraction of individual equilibria are illustrated and clearly show critical areas of multistability where a tiny drift in an initial point potentially induces jumps among different basins of attraction and coexisting states. Such multistability poses potential threats to engineering applications. The dynamical regions of hidden and self-excited attractors, and areas of stability of equilibria, are illustrated against two parameter spaces. Both illustrations reveal that two nonzero equilibrium points of the smooth cubic Chua's circuit have a transition from unstable to stable equilibrium points, leading to generations of self-excited and hidden attractors simultaneously. [ABSTRACT FROM AUTHOR]

This article discusses the multispiral Chua Chaotic attractor’s hidden bifurcations that are generated by the sine function. The number of spirals (also known as a multiscroll attractor) that are controlled by the integer parameter c can be used to describe the basic shape of chaotic attractors. Since this parameter is an integer, increasing it by one does not allow the observation of bifurcations from n to n + 2 spirals. The method of hidden bifurcations, however, enables the observation of such bifurcations by adding a real parameter ε. Chaotic attractors with either an even or an odd number of spirals are visible along the marked paths of bifurcation. Moreover, this additional hidden parameter allows finding the bifurcation of the multispiral Chua attractor from a stable state to a chaotic state. Furthermore, the Routh-Hurwitz criteria are used to study the stability of the original equilibrium point of the Chua attractor.

The article shows that transient chaos phenomena can be observed in a generalized memristor Chua's circuit where a nonlinear resistor is introduced to better model the real memristor behaviour. The flux‐charge analysis method is used to explain the origin of transient chaos, that is attributed to the drift of the index of the memristor circuit invariant manifolds caused by the charge flowing into the nonlinear resistor. [ABSTRACT FROM AUTHOR]

Explicit analytical solutions of higher-dimensional chaotic and hyperchaotic systems are areas of research to be much explored. Till now, the dynamics of higher-dimensional systems and the synchronisation dynamics of coupled higher-dimensional systems have not been studied analytically. In the present work, explicit analytical solutions are developed for the dynamical behaviours observed in third-order and fourth-order nonlinear dissipative systems and also for the coupled dynamics of these systems. The Chua's circuit and the modified canonical Chua's circuit are studied analytically in the present work. The analytical results explaining the underlying important features of these systems are validated through experimental results. [ABSTRACT FROM AUTHOR]

Stanford memristor model is a widely used model that accurately characterizes real non-volatile metal-oxide resistive random access memory (RRAM) devices with bipolar switching characteristics. The paper studies for the first time the dynamics and bifurcations in a class of nonlinear oscillators with real non-volatile memristor devices obeying Stanford model. This is in contrast with papers in the literature considering oscillators with ideal, abstract, or artificial memristor models, that are unable to describe physical memristors implemented in nanotechnology. One main new idea in the paper is to use the memristor as a programmable nonlinear resistor. Namely, two principal modes of operation are considered. 1) Analogue transient phase: the oscillator is designed so that in the transient oscillations the voltage on the memristor is below threshold, hence the main memristor state variable, i.e., the gap of the insulating material, is almost constant and the memristor behaves as a static nonlinear resistor. 2) Programming phase: the nonlinear characteristic of the memristor, which depends on the gap, can be changed via the application of voltages above threshold. The paper studies nonlinear oscillations in the transient phase for a fixed gap as well as the bifurcations phenomena displayed when the gap is varied. The paper also discusses the differences between the approach in the paper and those to design other memristor oscillators with non-volatile memristors.

This brief is concerned with the event-triggered stabilization for a memristor-based Chua’s circuits. A dynamic-periodic event-triggered approach is proposed, whose distinguishing feature is the introduction of two periodic triggering thresholds. One of the thresholds is an exponential decay function, and the other is an internal dynamic variable. Both thresholds contribute to the reduction of events. By Lyapunov theory, a concise criterion is developed for the stabilization of memristor-based Chua’s circuits. Simulation results are offered to support the theoretical results. [ABSTRACT FROM AUTHOR]

In this brief, the impulsive control problem is addressed for a class of unstable nonlinear systems under denial-of-service (DoS) attacks. A dynamic event-triggered impulsive control (DETIC) method is proposed to achieve asymptotic stability for the resulting closed-loop systems. A new class of impulsive control systems with dynamic event-triggered impulse instants are formulated, and some easily verifiable conditions are provided. The introduction of internal dynamic variable facilitates the regulation of the control frequency. Here, Zeno behaviors can be easily excluded by the proposed method. Finally, two examples, which include a Chua’s circuit and a numerical example, are given to demonstrate the efficiency of the method. [ABSTRACT FROM AUTHOR]

Abstract A scheme to implement the Jerk form of the Chua system family using a controllable canonical form applied in linear systems is proposed. The main thought is that the nonlinear function with a single independent variable input can be superposed by a multiple linear function, which is regarded as the input of the system, and its single variable is regarded as the output of the system. Its state space could be reconstructed into the controllable canonical form. The output after transformation is fed back to the nonlinear function as its input independent variable, thus the controllable canonical form is transformed into the Jerk form of the Chua’s chaotic system. All Jerk forms of three‐order Chua system, and part Jerk forms of four‐order Chua system are presented. Analysis of the Lyapunov exponent spectrum, eigenvalues of the original three‐order, four‐order Chua systems and their Jerk forms, and the same values demonstrate the equivalent of the systems for both structures. According to the complexity and National Institute of Standards and Technology (NIST) test results, the pseudo‐random performance of the chaotic sequence brought by the Jerk forms of the Chua system is better. The simplest unified circuit block diagram for the Jerk forms of the Chua’s family is also given. By changing their resistance parameters, the bifurcation diagrams show that Jerk forms’ systems are entering chaos, these circuits implement results of 2–6 scroll attractors. Experimental observations are provided for confirmation.

Copyright of Karaelmas Science & Engineering Journal / Karaelmas Fen ve Mühendislik Dergisi is the property of Karaelmas Science & Engineering Journal and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This brief studies the fixed/preassigned-time stability problems for a class of time-varying discontinuous system modeled by ordinary differential equation (ODE). By using a special exponential function and developing an indefinite derivative Lyapunov function method, the novel fixed-time stability (FXTS) and preassigned-time stability (PATS) criteria are established, where the settling-time (S-T) of FXTS is estimated and the preassigned-time is given for PATS. Then the established FXTS/PATS results are applied to achieve the fixed/preassigned-time stabilization of Chua’s circuit system (CCS) by designing switching external control input. [ABSTRACT FROM AUTHOR]

This article presents a simple and efficient masking technique based on Chua chaotic system synchronization. It includes feeding the masked signal back to the master system and using it to drive the slave system for synchronization purposes. The proposed system is implemented in a field programmable gate array (FPGA) device using the Xilinx system generator tool. To achieve synchronization, the Pecora-Carroll identical cascading synchronization approach was used. The transmitted signal should be mixed or masked with a chaotic carrier and can be processed by the receiver without any distortion or loss. For different images, the security analysis is performed using the histogram, correlation coefficient, and entropy. In addition, FPGA hardware co-simulation based Xilinx Artix7 xc7a100t-1csg324 was used to check the reality of the encryption and decryption of the images. [ABSTRACT FROM AUTHOR]

Memory resistor, or memristor, has been realized as a discrete electronic device and has a perspective application in the field of cryptography. The physical implementation of the memristor in chaotic circuits has been scarcely explored. In this paper, a memristor is fabricated by spin-coating a cobalt ferrite precursor on a processed silicon and is then electro-sputtered with silver to act as the anode with the base silicon as the cathode. This fabrication process has a scalability potential in conjunction with integrated circuit fabrication techniques and complementary metal oxide semiconductor (CMOS) technologies. The fabricated cobalt ferrite memristor has shown a ratio between the on and off resistance of >1000 and has been implemented in a chaotic Chua's circuit, making it one of few physical implementations of a physical memristor in a physical circuit. The analysis and characterization of this circuit using bifurcation diagrams and Lyapunov exponent prove the chaotic behavior of a real Chua's circuit. This chaotic behavior can be useful in chaotic cryptography as nonperiodic oscillations can be leveraged to make sensitive information more difficult to interpret by bad actors. [Display omitted] • A memristor is constructed on silicon to make fabrication process more scalable. • The memristor consists of spin-coated cobalt ferrite layer with active electrodes. • The memristor is implemented in Chua's circuit that exhibits chaotic behavior. • Chaotic behavior is proven with bifurcation and Lyapunov exponent analysis. [ABSTRACT FROM AUTHOR]

Copyright of Electric Machines & Control / Dianji Yu Kongzhi Xuebao is the property of Electric Machines & Control and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This study aims to design a new architecture of the artificial neural networks (ANNs) using the Xilinx system generator (XSG) and its hardware co-simulation equivalent model using field programmable gate array (FPGA) to predict the behavior of Chua’s chaotic system and use it in hiding information. The work proposed consists of two main sections. In the first section, MATLAB R2016a was used to build a 3×4×3 feed forward neural network (FFNN). The training results demonstrate that FFNN training in the Bayesian regulation algorithm is sufficiently accurate to directly implement. The second section demonstrates the hardware implementation of the network with the XSG on the Xilinx artix7 xc7a100t-1csg324 chip. Finally, the message was first encrypted using a dynamic Chua system and then decrypted using ANN’s chaotic dynamics. ANN models were developed to implement hardware in the FPGA system using the IEEE 754 Single precision floating-point format. The ANN design method illustrated can be extended to other chaotic systems in general. [ABSTRACT FROM AUTHOR]

Coupled arrays of Chua's circuit have been studied extensively. The system admits traveling front, back, pulse as well as periodic and chaotic waves. However, the stability problem of these waves has rarely been investigated. In this paper, we consider the PDE approximation of the system and prove for the PDE that the traveling back is nonlinearly stable. The question of stability can be reduced to an eigenvalue problem in R 4. The Evans function method is applied, along with the geometric singular perturbation theory and the smooth linearization. [ABSTRACT FROM AUTHOR]

This brief focus on the event-triggered synchronization of networked chaotic Lur’e systems. To relieve the burden of communication network with limited bandwidth, a novel memory-based event-triggered mechanism with the past information of the system is presented. The synchronization error system under the memory-based event-triggered mechanism is modeled by a distributed delay system. Applying an integral inequality based on Legendre polynomials, a novel synchronization condition is derived via linear matrix inequalities. Finally, a Chua’s circuit is adopted to illustrate the advantage of the proposed control strategy. [ABSTRACT FROM AUTHOR]