Memristive Chaotic Circuit Research Articles

A novel memristive chaotic jerk circuit and its microcontroller-based sliding mode control

Due to the experimental realization of memristor circuit elements, research on memristors and memristor-based circuits has surged. Because of their nonvolatile and nonlinear behavior, memristors can be easily applied to chaotic circuits. This study introduces a novel memristive 3D chaotic jerk system, comprising only seven terms, along with its electronic model and microcontroller-based control. The flux-controlled memristor-based jerk system exhibits complex dynamics, which were analyzed through various properties such as phase portraits, the Jacobian matrix, equilibria, eigenvalues, Lyapunov spectra, bifurcation diagrams, and transient chaos behavior. Three controllers, namely, nonlinear feedback, classical sliding mode, and integral sliding mode were designed to control the chaotic jerk oscillator. Lyapunov functions were used to synthesize the nonlinear feedback controller and ensure system stability with the sliding mode technique. Numerical tests under various performance criteria and disturbance conditions showed that the sliding mode controller outperforms the nonlinear feedback controller due to its single-state control structure. The chaotic jerk oscillator hardware circuit was designed and implemented, operating easily with initial conditions set to zero and low DC supply voltages, with all output voltages within ±6V. Both theoretical and simulation results demonstrate the system’s complexity and applicability, with experimental results aligning well with simulations. Consequently, effective microcontroller-based control was achieved using a single-state controller.

Dynamical analysis and synchronization control of flux-controlled memristive chaotic circuits and its FPGA-Based implementation

This paper focuses on addressing the synchronization control problem of memristive chaos through the investigation of a single feedback controller strategy. Our objective is to deploy this strategy on field-programmable gate arrays (FPGA) with the aim of bolstering the security and reliability of memristive chaotic synchronization control. Concurrently, we seek to enhance system performance and fulfill the diverse requirements of various applications. Initially, the study utilizes chaos synchronization theory and the Routh–Hurwitz stability criterion to devise a feedback controller with a single input. This controller plays a crucial role in establishing a synchronization system specifically designed for memristive chaos. Subsequently, the FPGA design approach utilizing DSP Builder is employed to create models for both the single-input feedback controller and the memristive chaotic synchronization control system. This approach facilitates the efficient translation of these theoretical concepts into practical digital circuit implementations. Finally, the paper concludes with an experimental analysis that verifies the feasibility and practical applicability of the FPGA circuit design for memristive chaotic synchronization control.

A Novel Fractional-Order Memristive Chaotic Circuit with Coexisting Double-Layout Four-Scroll Attractors and Its Application in Visually Meaningful Image Encryption

This paper proposes a fractional-order chaotic system using a tri-stable locally active memristor. The characteristics of the memristor, dynamic mechanism of oscillation, and behaviors of the proposed system were analyzed, and then a visually meaningful image encryption scheme was designed based on the chaotic system, DNA encoding, and integer wavelet transform (IWT). Firstly, the mathematical model of the memristor was designed, which was nonvolatile, locally active, and tri-stable. Secondly, the stability, dynamic mechanism of oscillation, bifurcation behaviors, and complexity of the fractional-order memristive chaotic system were investigated and the conditions of stability were obtained. Thirdly, the largest Lyapunov exponent, bifurcation diagram, and complexity of the novel system were calculated and the coexisting bifurcation, coexisting attractors, spectral entropy, and so on are shown. Finally, a visually meaningful image encryption scheme based on the proposed system was designed, and its security was assessed by statistical analysis and different attacks. Numerical simulation demonstrated the effectiveness of the theoretical analysis and high security of the proposed image encryption scheme.

Memristive chaotic circuits and systems

Memristive chaotic circuits and systems

Fracmemristor Oscillator: Fractional-Order Memristive Chaotic Circuit

In this paper, the Fractional-Order Memristive Chaotic Circuit (FMCC) is proposed to be achieved by the fracmemristor, which is a portmanteau of “fractional-order” and “memristor”. Considering the unique fingerprints and nonlinearities of fracmemristors, it is natural to ponder a challenging theoretical problem to generalize the Integer-Order Memristive Chaotic Circuit (IMCC) to the FMCC. Motivated by this inspiration, the paper proposes an FMCC by replacing the diode in Chua’s chaotic circuit with a fracmemristor and a negative resistor in parallel. To simplify analysis, a new Cubic Nonlinear Voltage-Controlled Capacitive Ladder Scaling Fracmemristor (CVCLF) is proposed to implement the FMCC. New fingerprints are found in the CVCLF. Compared with the IMCC, dynamical behaviors of the FMCC are not only related to circuit parameters and initial conditions, but also related to the circuit stage and the operational order. The FMCC provides two extra degrees of freedom. Numerical simulations and hardware experiments demonstrate that the FMCC has multistability, transient chaos, state transition phenomena, etc. A significant advantage of the FMCC is that it possesses the fractional-order-sensitivity characteristic, which represents its dynamical behaviors change with the operational order. The proposed FMCC is the first application of fracmemristors in chaos.

Memristive band pass filter chaotic circuit: multistability and control

ABSTRACT This paper studies the influence of an explicit symmetry break on the dynamics of a memristive band pass filter. It is shown that the circuit exhibits complex behaviours. The symmetry break is achieved by considering a memristor emulator with an asymmetric current-voltage characteristic. We describe how the bifurcation sequences, the number and types of coexisting solutions, and the topology of the basins of attraction metamorphose when monitoring both the system parameters and initial conditions. The theoretical results are validated by a series of simulations under PSPICE.

Real-time fuzzy-pid synchronization of memristor-based chaotic circuit using graphical coded algorithm in secure communication applications

The main goal of this study is to implement real-time synchronization of a memristor-based chaotic circuit for secure communication on LabVIEW virtual instrument environments. Memristors can be used in chaotic circuits because of their nonlinear behavior. In this paper, an application for secure communication systems is proposed by using the chaotic property of the memristor. Phase portraits, Lyapunov exponential spectrum, and bifurcation diagrams of the memristor-based chaotic circuit were investigated. A Fuzzy-PID controller was used for master-slave synchronization of memristive chaotic circuit and in secure communication application, three images were also used for encryption and decryption. NI 6251 DAQ card was used to obtain real-time results. Information entropy values, correlation coefficients (CC), peak signal to noise ratio (PSNR), structural similarity index (SSIM), correlation coefficients for the horizontal, vertical and diagonal directions from the three encrypted images, number of pixels change rate (NPCR) and unified average changing intensity (UACI) are calculated to test encryption/decryption performance in the designed system. The results obtained from real-time applications and simulations prove that memristor-based chaotic circuits can be used in secure communication systems where privacy is important.

A memristive conservative chaotic circuit with two different offset boosting behaviors

Recent studies have shown that more complex dynamics could be observed if memristors are coupled into nonlinear circuits. To date, however, far too little attention has been paid to memristor-based high-dimensional conservative systems. Previous research on the low-dimensional mem-element system has suffered from a paucity of rich dynamical characteristics. In addition, the physical implementation of conservative systems requires higher accuracy than dissipative ones, and no DSP implementation of a memristor-based conservative system is available. In this paper, a high-dimensional memristive conservative system is built by coupling the linear resistance of a conservative chaotic circuit with a flux-controlled memristor. Compared to the existing conservative systems, the proposed system exhibits a variety of quasi-periodic topologies and has two offset boosting behaviors. One of the constant variable offset boosting also presents meaningful parameter space expansion characteristics. And the other initial offset boosting exhibits homomorphic and heteromorphic multistability properties. Moreover, our work also reveals that transient chaos is the route to chaos in conservative systems. Finally, analog circuit simulation and DSP-based digital circuits verify the correctness of the numerical calculation and the physical implementations of the system.

Extreme Multistability and Antimonotonicity in a Shinriki Oscillator with Two Flux-Controlled Memristors

This paper proposes a novel memristive chaotic circuit which originated from a Shinriki oscillator with two flux-controlled memristors of different polarities. This two-memristor-based Shinriki oscillator (TMSO) having a special plane equilibrium is prone to exhibiting the initial-dependent phenomenon of extreme multistability. To investigate its internal dynamics, a third-order dimensionality reduction model is established by utilizing the constitutive relationship of its memristor’s flux and charge. The uncertain plane equilibrium is transfered into some deterministic model that can accurately predict the dynamical evolution of the system, where interesting phenomena of asymmetric bifurcations, extreme multistability and antimonotonicity are detected and analyzed by evaluating the position and stability of the equilibria in the flux–charge model. The simulation is carried out via Multisim to validate the analysis model, and the comparison of the phase trajectories, before and after dimensionality reduction, shows that this oscillator is good for research and practical use.

Dynamic Behaviors Analysis of a Novel Fractional-Order Chua’s Memristive Circuit

This paper proposed a novel fractional-order Chua’s memristive circuit. Firstly, a fractional-order mathematical model of a diode bridge generalized memristor with RLC filter cascade is established, and simulations verify that the fractional-order generalized memristor satisfies the basic characteristics of a memristor. Secondly, the capacitor and inductor in Chua’s chaotic circuit are extended to the fractional order, and the fractional-order generalized memristor is used instead of Chua’s diode to establish the fractional-order mathematical model of chaotic circuit based on RLC generalized memristor. By studying the stability analysis of the equilibrium point and the influence of the circuit parameters on the system dynamics, the dynamic characteristics of the proposed chaotic circuit are theoretically analyzed and numerically simulated. The results show that the proposed fractional-order memristive chaotic circuit has gone through three states: period, bifurcation, and chaos, and a narrow period window appears in the chaotic region. Finally, the equivalent circuit method is adopted in PSpice to realize the construction of the fractional-order capacitance and inductance, and the simulation of the fractional-order memristive chaotic circuit is completed. The results further verify the correctness of the theoretical analysis.

A coupling method of double memristors and analysis of extreme transient behavior

By coupling a variable of the memristor in one memristive chaotic circuit with another memristor, an approach to construct a high-dimensional memristive chaotic system is proposed and a five-dimensional hidden chaotic system with double memristors is obtained. The Lyapunov fractal dimension and dynamics map of the system demonstrate that the system has extreme transient behaviors, such as chaos to period, chaos to quasi-period, quasi-period to another quasi-period, quasi-period to chaos, and chaos to another kind of chaos. The whole transition process experiences as many as 2, 3, 4, or even 5 different status. Besides, an interesting symmetric transient phenomenon is discovered and extreme multistability is also observed when changing the initial conditions. The extreme transient behavior is validated using the spectral entropy algorithm.

An Image Compression and Encryption Algorithm Based on the Fractional-Order Simplest Chaotic Circuit

Based on compressive sensing and fractional-order simplest memristive chaotic system, this paper proposes an image compression and encryption scheme. First, a fractional-order simplest memristive chaotic circuit system is designed. The dynamic characteristics of the chaotic system are analyzed by the phase diagram, the Lyapunov exponent's spectrum, and the bifurcation diagram to determine the parameters and pseudo-random sequences used in the encryption scheme. Secondly, an encryption scheme based on compressive sensing is designed. This scheme compresses the image twice to fully reduce the storage cost, and scrambles the pixel matrix twice through block scrambling and zigzag transformation, and then uses chaotic pseudo-random sequence and GF (17) domain diffusion image matrix to obtain the final cipher image. Finally, simulation results and performances analysis indicate that the scheme still has good reconstruction performance, even when the compression ratio is 0.25, and the security analysis shows that it can resist various attacks and has high security.

Data-Based H∞Control for the Constrained-Input Nonlinear Systems and its Applications in Chaotic Circuit Systems

In this paper, $H_\infty $ control problem is investigated by off-policy integral reinforcement learning (IRL) method for the nonlinear systems with completely unknown dynamics, disturbances, and constrained-input. Firstly, according to a model-based policy iteration (PI) algorithm, a model-free algorithm is proposed based on the derived iterative equation, and the equivalence of model-based PI algorithm and model-free algorithm is proven. Then, the model-free algorithm is implemented by off-policy IRL technology to solve the Hamilton-Jacobi-Isaacs (HJI) equation with the collected system data by the least-square approach, where three neural networks (NNs) are constructed to approximate the value function, control and the disturbance. Finally, our proposed methods are applied to stabilize an autonomous third-order Chua’s chaotic circuit system and a non-autonomous second-order memristive chaotic circuit system to illustrate the efficiency of the proposed method.

A memristive conservative chaotic circuit consisting of a memristor and a capacitor

In this paper, a new memristor model is proposed and the corresponding emulator is presented to explore its electrical characteristics. A memristive chaotic circuit is designed based on this memristor and a capacitor, which has a conservative nature. The dynamic properties of the system, including high sensitivity to initial values and parameters, coexisting orbits, and transient phenomena, are obtained and investigated by Lyapunov exponents and phase volumes. The chaotic characteristics of the system are confirmed by circuit simulations and experimental devices, which illustrate the validity of the theoretical analyses. Furthermore, a random sequence generator is developed to explore the potential application of the circuit.

A new chaotic circuit with multiple memristors and its application in image encryption

In this paper, a new seventh-order mixed memristive chaotic circuit was designed, and the new mathematical model of the system was established. The origin as the only equilibrium point was calculated. Based on the chaotic secret key generated by the memristive chaotic circuit system, the new algorithm of the image encryption was designed. In particular, by using the security analysis methods of gray histogram, correlation and robustness, the security feature of the new encryption algorithm was analyzed. And the results show that the encryption algorithm based on this mixed memristive chaotic system has higher security and better anti-decoding ability. In comparison with the simple model of the memristive chaotic circuit, this new memristive chaotic circuit model has complete RLC structure and multiple memristors. It is closer to the actual memristive chaotic circuit. Thus, it is of great significance to the commercial realization of the memristive circuit. In particular, the memristive chaotic system also provides a valuable model of the system for the research of the related fields.

Bursting oscillations and coexisting attractors in a simple memristor-capacitor-based chaotic circuit

The design and analysis of a simple autonomous memristive chaotic circuit are important in theoretical, numerical, and experimental demonstrations of complex dynamics. In this paper, a simple autonomous memristive circuit is implemented, which only consists of an active second-order memristive diode bridge and a capacitor. Based on the available circuit, the mathematical model is established and its symmetry, dissipativity, and equilibrium stability are analyzed. Numerical simulations show that the proposed circuit exhibits complex behaviors of unipolar periodic and chaotic bursting oscillations along with coexisting attractors. It is worth noting that the circuit exhibits such a special bursting behavior previously unobserved in third-order autonomous memristive circuits. Moreover, spectral entropy complexities are calculated to provide an intuitive and effectual method for the circuit parameter configurations. The circuit simulations and hardware experiments verify the theoretical analyses and numerical simulations.

Characteristics Analysis of the Fractional-Order Chaotic Memristive Circuit Based on Chua’s Circuit

In this paper, a new fractional-order memristive circuit is defined based on canonical Chua’s circuit and Voltage-controlled memristor model. The fractional-order chaotic system is solved by conformable Adomian decomposition method (CADM), and the complexity characteristics are analyzed through sample entropy (SampEn) algorithm. The complexity analysis results correspond to the bifurcation diagram and Lyapunov exponential spectrum, which shows that SampEn algorithm can effectively reflects complexity of chaotic system. What’s more, the chaos diagrams of complexity with the two parameters variation and the three parameters variation are analyzed. The numerical simulation result indicates that the system parameters variable complexity can effectively reflect the randomness of the fractional-order chaotic system, and the system has rich dynamical performances. It provides the theoretical guidance and experimental evidence for fractional-order memristive chaotic circuit application in cryptography and secure communication.

Impulsive anti-synchronization control for fractional-order chaotic circuit with memristor

This paper investigates the anti-synchronization of fractional-order memristive chaotic circuits (FMCC) with time delay via an impulsive control scheme. Based on the Mittag-Leffler function, the impulsive control principle and the Lyapunov stability theory, several criteria are adopted to derive the impulsive anti-synchronization of FMCC with time delay. Finally, numerical examples are exploited to verify the effectiveness of the theoretical analysis, and some discussions about the stable region are given.

A true random bit generator based on a memristive chaotic circuit: Analysis, design and FPGA implementation

The aim of this paper is to present a true random bit generator (TRBG) based on a memristive chaotic circuit and its implementation on Field Programmable Gate Array (FPGA) board. The proposed TRBG architecture makes use of a memristive canonical Chua's oscillator and a logistic map as entropy sources, while the XOR function is used for post-processing. The optimal parameter set for the chaotic systems has been chosen by carrying out numerical simulations of the system and adopting the scale index parameter to determine the degree of non-periodicity of the obtained bit streams. The proposed TRBG system has been then modeled and co-simulated on the Xilinx System Generator (XSG) platform and implemented on the Xilinx Kintex-7 KC705 FPGA Evaluation Board, obtaining experimental results in agreement with the expectations. Finally, the system has been validated with statistical analysis by using the NIST 800.22 statistical test suite.

Color Image Compression-Encryption Algorithm Based on Fractional-Order Memristor Chaotic Circuit

In this paper, a fractional-order memristive chaotic circuit system is defined according to memristor circuit. The dynamic characteristics are analyzed through the phase diagram, bifurcation diagram, and Lyapunov exponent spectrum, and the randomness of the chaotic pseudo-random sequence is tested by NIST SP800-22. Based on this fractional-order memristive chaotic circuit, we propose a novel color image compression-encryption algorithm. In this algorithm, compression sensing (CS) algorithm is used for compression image, and then using Zigzag confusion, add modulus and BitCircShift diffuse encrypt the image. The theoretical analysis and simulation results indicate that the proposed compression and encryption scheme has good compression performance, reconstruction effect, and higher safety performance. Moreover, it also shows that the new algorithm facilitates encryption, storage, and transmission of image information in practical applications.