Memristive Hyperchaotic System Research Articles

Dynamic Analysis and Field-Programmable Gate Array Implementation of a 5D Fractional-Order Memristive Hyperchaotic System with Multiple Coexisting Attractors

On the basis of the chaotic system proposed by Wang et al. in 2023, this paper constructs a 5D fractional-order memristive hyperchaotic system (FOMHS) with multiple coexisting attractors through coupling of magnetic control memristors and dimension expansion. Firstly, the divergence, Kaplan–Yorke dimension, and equilibrium stability of the chaotic model are studied. Subsequently, we explore the construction of the 5D FOMHS, introducing the definitions of the Caputo differential operator and the Riemann–Liouville integral operator and employing the Adomian resolving approach to decompose the linears, the nonlinears, and the constants of the system. The complex dynamic characteristics of the system are analyzed by phase diagrams, Lyapunov exponent spectra, time-domain diagrams, etc. Finally, the hardware circuit of the proposed 5D FOMHS is performed by FPGA, and its randomness is verified using the NIST tool.

Dynamic analysis based on a memristive hyperchaotic system with stable unfixed point and its synchronization application

A novel two-memristor hyperchaotic system is obtained by introducing a cubic magnetic-controlled memristor and a hyperbolic sine function memristor. The dynamics of the new system are analyzed by various techniques such as Lyapunov exponents, complexity, 0–1 test, bifurcation diagram and phase diagram. The results demonstrate that the new system exhibits complex dynamic behaviors, including transient chaos, transient transition, intermittent chaos, and offset-boosting. Notably, a rare phenomenon with stable unfixed point has been discovered in this newly proposed system. The largest Lyapunov exponent of the stable unfixed point fluctuates around 0 and remains predominantly less than or equal to 0. Despite this, the new system still partially exhibits chaotic characteristics, indicating that the stable unfixed point can be regarded as a local chaotic attractor. Furthermore, there are four types of coexisting attractors with period-period, chaos-chaos, chaos-stable unfixed point and stable unfixed point-stable unfixed point in the new system. The circuit design is implemented to validate the accuracy of the memristive chaotic system, and the consistency between numerical calculations and simulation results is confirmed. Finally, the coupling synchronization and tracking synchronization methods are designed, which hold practical applications in the field of secure communication, control systems and signal processing.

A novel 4D memristor-based hyperchaotic system with hidden attractors: Dynamics, periodic orbits analysis, and DSP realization

As a controllable nonlinear component, memristors are easy to generate chaotic signals, and memristor-based hyperchaotic systems are currently a hot research topic. This paper constructs a novel 4D memristive hyperchaotic system, where the presence of trigonometric functions improved system complexity, enabling it to generate richer and more complex dynamic behaviors. The proposed memristive hyperchaotic system has no equilibrium point, thus the corresponding attractors belong to hidden attractors. We discussed the bifurcation behaviors as the system varies with parameters, transient phenomena, 0−1 test, and extreme homogeneous multistability of the system. In addition, complexity analyses based on the SE and C0 algorithms were investigated. Furthermore, the unstable periodic orbits of the system were analyzed, appropriate symbol encodings were established, and the pruning rules and periodic distribution patterns of the cycles were explored. Finally, the new system was experimentally validated using the DSP digital circuit, and the results were consistent with numerical simulations. Therefore, the new system has complex dynamic characteristics, which have a wide range of applications in the fields of secure communication and image encryption.

A 5-D memristive hyperchaotic system with extreme multistability and its application in image encryption

By coupling memristors to nonlinear circuits, more complex dynamical behaviors can be induced. However, to date, there has been insufficient attention given to high-dimensional chaotic systems based on memristors. In this paper, a magnetic-controlled memristor is combined with a three-dimensional chaotic system, resulting in a five-dimensional memristive chaotic system. Through dynamic analysis and numerical simulations, the chaotic nature of the system is elucidated based on fundamental system behaviors, including Lyapunov dimension, dissipativity, stability of equilibrium points, 0–1 test, and Poincaré mapping. During the complex dynamical analysis of this system, unique dynamical behaviors are discovered, including intermittent chaos, transient chaos, extreme multistability, and offset-boosting. Moreover, the consistency between numerical calculations and the physical implementation of the actual system is verified through equivalent circuit design. Finally, this system is applied to image encryption, leading to the design of an efficient and secure hyper-chaotic image encryption algorithm, whose effectiveness is confirmed through several security tests.

A hyperchaotic memristive system with extreme multistability and conservativeness

A hyperchaotic memristive system with extreme multistability and conservativeness

Offset boosting in a memristive hyperchaotic system

In this article, an autonomous memristive hyperchaotic system with multi-dimensional offset boosting is constructed and analyzed. Besides this, the oscillation can be rescaled by an independent controller in the memristor. Two independent constants are obtained for offset boosting with one or two variables, which provide two modes of offset boosting, including single control and synchronous reverse control. In addition, the offset of the variables is also modified by the system bifurcation parameters or combined with amplitude control. The multistability can also be identified according to the offset boosting. Finally, circuit implementation based on PCB is proposed to confirm the numerical simulations.

Video encryption via synchronization of a fractional order T-S fuzzy memristive hyperchaotic system

Video encryption via synchronization of a fractional order T-S fuzzy memristive hyperchaotic system

Optical image encryption algorithm based on a new four-dimensional memristive hyperchaotic system and compressed sensing

Some existing image encryption schemes use simple low-dimensional chaotic systems, which makes the algorithms insecure and vulnerable to brute force attacks and cracking. Some algorithms have issues such as weak correlation with plaintext images, poor image reconstruction quality, and low efficiency in transmission and storage. To solve these issues, this paper proposes an optical image encryption algorithm based on a new four-dimensional memristive hyperchaotic system (4D MHS) and compressed sensing (CS). Firstly, this paper proposes a new 4D MHS, which has larger key space, richer dynamic behavior, and more complex hyperchaotic characteristics. The introduction of CS can reduce the image size and the transmission burden of hardware devices. The introduction of double random phase encoding (DRPE) enables this algorithm has the ability of parallel data processing and multi-dimensional coding space, and the hyperchaotic characteristics of 4D MHS make up for the nonlinear deficiency of DRPE. Secondly, a construction method of the deterministic chaotic measurement matrix (DCMM) is proposed. Using DCMM can not only save a lot of transmission bandwidth and storage space, but also ensure good quality of reconstructed images. Thirdly, the confusion method and diffusion method proposed are related to plaintext images, which require both four hyperchaotic sequences of 4D MHS and row and column keys based on plaintext images. The generation process of hyperchaotic sequences is closely related to the hash value of plaintext images. Therefore, this algorithm has high sensitivity to plaintext images. The experimental testing and comparative analysis results show that proposed algorithm has good security and effectiveness.

Privacy data protection scheme using memristive hyperchaos and multi-scale block compressive sensing

Recently, most meaningful image encryption schemes incorporated with various compressive sensing models have been developed to achieve dual protection of private image data and appearance. However, there exist performance constraints in these schemes in terms of anti-chosen-plaintext attack capability and key management. Aiming at the above issues, a new visually secure image encryption scheme is proposed using multi-scale block compressive sensing (MSB-CS) model and asymmetric integer wavelet transform (IWT) embedding. In this scheme, a memristor model with locally active tristable is first introduced into the oscillator to construct a new 5D memristive hyperchaotic system to generate cipher flows. Then, the non-linear MSB-CS model is designed to compress sparsely-represented plaintext coefficients. After a series of encryption operations, secret image without semantic features is asymmetrically embedded into the same-scale non-secret-involved carrier image. Additionally, both communicating parties, Alice and Bob, acquire shared secret key through the key sharing protocol based on matrix factorization problem. Finally, simulation experiments and comprehensive analysis indicate that the 5D memristive system has complicated hyperchaotic behaviours. In the meantime, the designed encryption scheme possesses better the anti-differential attack capability and reconstruction performance than other recently proposed schemes.

Preface

The 14th Five-Year Plan clearly points out that we should adhere to the core position of innovation in the overall situation of modernization, regard scientific and technological self-reliance and self-improvement as the strategic support for national development. At present, from a global perspective, science and technology have increasingly become the main force to promote economic and social development, and innovation is the trend of the times. In the fierce international competition, only innovators advance, only innovators are strong, and only innovators win.However, the foundation of China’s scientific and technological innovation is not yet solid, there is still a significant gap in the level of innovation, and in some fields the gap has not narrowed, but has a tendency to expand. Therefore, improving innovation capabilities and creating an innovation ecology are the top priorities for building an innovative country and a world science and technology power.The International Conference on Mechanical Engineering and Automation (MEA 2022), as a sub-venue of the 4th International Conference on Scientific and Technological Innovation, was held in Chongqing, China on December 9th to 11th, 2022 via virtual form.MEA 2022 focused on the latest research and technology of Mechanical Engineering and Automation to discuss the innovation and development in these fields, and to create a forum for students, scholars, engineers, participants to give reports, share ideas as well as get new advice and insights from each other. It brought together about 150 participants. Many renowned professors delivered dramatic keynote speeches during the conference. One of them, Chunbo Xiu, a Professor from Tiangong University, China, shared a report on Design and Circuit Implementations of Memristor Hyperchaotic System. To enhance the order and Kolmogorov entropy of the memristive hyperchaotic system and improve the realizability of the circuit, a memristive hyperchaotic system that consists of two flux-controlled memristors and one charge-controlled memristor was designed. Combined with Lyapunov exponential spectrum, phase trajectory diagram and bifurcation diagram, dynamic characteristics of the system were analyzed, and the effects of system control parameters and initial state on the system dynamic behavior were explored.This volume covers topics on all fields of research related to Mechanical Engineering and Automation, including Mechatronics, Intelligent Control, Vehicle Engineering, Detection and Sensing Technology, Intelligent Optimization Algorithms, etc., increasing the number of scientific publications for science and technology innovation in related fields.We would like to thank all the participants in the International Conference on Mechanical Engineering and Automation. We would also like to thank the Conference Chairs, all the Technical Program Committee and Organizing Committee members, for the work and preparation they put in to organize this event. Finally, our special acknowledgements go to the Journal of Physics: Conference Series, for the endeavor of all its colleagues in publishing this paper volume.The Committee of MEA 2022List of Committee Member is available in this pdf.

Multiple mixed state variable incremental integration for reconstructing extreme multistability in a novel memristive hyperchaotic jerk system with multiple cubic nonlinearity

Memristor-based chaotic systems with infinite equilibria are interesting because they generate extreme multistability. Their initial state-dependent dynamics can be explained in a reduced-dimension model by converting the incremental integration of the state variables into system parameters. However, this approach cannot solve memristive systems in the presence of nonlinear terms other than the memristor term. In addition, the converted state variables may suffer from a degree of divergence. To allow simpler mechanistic analysis and physical implementation of extreme multistability phenomena, this paper uses a multiple mixed state variable incremental integration (MMSVII) method, which successfully reconstructs a four-dimensional hyperchaotic jerk system with multiple cubic nonlinearities except for the memristor term in a three-dimensional model using a clever linear state variable mapping that eliminates the divergence of the state variables. Finally, the simulation circuit of the reduced-dimension system is constructed using Multisim simulation software and the simulation results are consistent with the MATLAB numerical simulation results. The results show that the method of MMSVII proposed in this paper is useful for analyzing extreme multistable systems with multiple higher-order nonlinear terms.

Design and Implementation of a Novel Circuit-Based Memristive Non-autonomous Hyperchaotic System with Conservative and Offset Boosting for Applications to Image Encryption

Design and Implementation of a Novel Circuit-Based Memristive Non-autonomous Hyperchaotic System with Conservative and Offset Boosting for Applications to Image Encryption

Dynamic Analysis and FPGA Implementation of a New, Simple 5D Memristive Hyperchaotic Sprott-C System

In this paper, we first present a simple seven-term 4D hyperchaotic system based on the classical Sprott-C 3D chaotic system. This novel system is inspired by the simple 4D hyperchaotic system based on Sprott-B proposed by A. T. Sheet (2022). We discuss the phenomenon of premature divergence brought about by the improper choice of coupling parameters in that paper and describe the basic properties of the new system with phase diagrams, Lyapunov exponential spectra and bifurcation diagrams. Then, we find that the dynamical behaviors of the system suffer from the limitation of the control parameters and cannot represent the process of motion in detail. To improve the system, we expand the dimensionality and add the control parameters and memristors. A 5D memristive hyperchaotic system with hidden attractors is proposed, and the basic dynamical properties of the system, such as its dissipation, equilibrium point, stability, Lyapunov exponential spectra and bifurcation diagram, are analyzed. Finally, the hardware circuits of the 4D Sprott-C system and the 5D memristive hyperchaotic system were realized by a field programmable gate array (FPGA) and verified by an experiment. The experimental results are consistent with the numerical simulation results obtained in MATLAB, which demonstrates the feasibility and potential of the system.

Dynamics analysis, FPGA realization and image encryption application of a 5D memristive exponential hyperchaotic system

The exponential function is one of the basic elementary functions, which plays an irreplaceable role in mathematics and is also widely used in practical activities such as life and production. In this paper, a new 5D memristive exponential hyperchaotic system (MEHS) is proposed, which includes an exponential term and a nonlinear flux-controlled memristive model. Fundamental dynamics characteristics of the system are analyzed using phase diagram, Lyapunov exponential spectrum and bifurcation diagram. When appropriate parameter sets are selected, the MEHS exhibits a rich set of dynamic behaviors, including the coexistence of periodic and periodic attractors, periodic and chaotic attractors, chaotic and hyperchaotic attractors. In addition, the Field Programmable Gate Array (FPGA) is used to realize the 5D MEHS, and the experimental results are consistent with the numerical simulation results on MATLAB. Finally, an image encryption application based on the 5D MEHS is presented. The security analysis shows the feasibility and effectiveness of the image encryption algorithm.

Dynamic analysis and circuit realization of a novel variable-wing 5D memristive hyperchaotic system with line equilibrium

By introducing flux-controlled memristor and linear feedback term into the three-dimensional (3D) chaotic system, and using the state feedback control method to increase dimension, a novel variable-wing 5D memristive hyperchaotic system has been proposed in this paper. The proposed memristive hyperchaotic system has a line equilibrium point whose position is directly determined by the control parameter. The remarkable feature of the system is that the influence of positive feedback memristor and negative feedback memristor on the system and their similarities and differences are considered. Meanwhile, by analyzing the complex dynamic behavior of the system under different control parameters and initial values, it can be found that the proposed memristive hyperchaotic system shows many interesting phenomena including hidden extreme multistability, transient chaotic transition behavior and variable-wing characteristics. Finally, the hardware electronic circuit of the memristive hyperchaotic system is designed. The hardware experimental results are highly consistent with the numerical simulation ones, which demonstrate the physical realizability of the proposed system.

Design and circuit implementations of multimemristive hyperchaotic system

To enhance the order and Kolmogorov entropy of the memristive hyperchaotic system and improve the realizability of the circuit, a sixth-order memristive hyperchaotic system that consists of two flux-controlled memristors and one charge-controlled memristor is designed. Combined with Lyapunov exponential spectrum, phase trajectory diagram and bifurcation diagram, dynamic characteristics of the system are analyzed, and the effects of system control parameters and initial state on the system dynamic behavior are explored. Equivalent circuit models of flux-controlled and charge-controlled memristors with cubic nonlinear characteristics are constructed by the basic operation modules, and the hardware simulation design of the memristive hyperchaotic system is completed. The experimental results show that the proposed system can exhibit kinds of attractors, such as periodic-loop, single-scroll, double-scroll and superposition by adjusting system control parameters, and the system can show the behavior of period doubling bifurcation entering chaos and anti-period doubling exiting chaos under the different system initial states, which corresponds to the multistable coexistence phenomena of the system, such as quasi-period and hyperchaos. Meanwhile, the sixth-order hyperchaotic system is implemented by hardware circuit simulation. The phase diagrams of the circuit simulation are consistent with that of the numerical simulation, which verifies the physical realizability of the hyperchaotic system. Based on the strong initial value sensitivity and large K entropy, the memristive hyperchaotic system can be applied to the image encryption, and the confidentiality and security of images can be effectively enhanced.

Design and circuit implementation of a novel 5D memristive CNN hyperchaotic system

In order to enrich the dynamic characteristics of cellular neural network (CNN) and reveal the influence of memristor nonlinearity on the dynamic behavior of the network, a novel five-dimension memristive cellular neural network hyperchaotic system is designed by replacing the linear resistors in the output module of cellular neural network with two flux-controlled memristors, and the hardware circuit design of the system is completed. Based on Lyapunov exponent spectrum and attractor phase trajectories, the effects of system parameters and initial value on the dynamic characteristics of the memristive cellular neural network model are studied, and the generation conditions of different chaotic attractors and coexisting chaotic attractors are explained. Kolmogorov entropy is used to measure the chaotic degree of the system when the parameters are in different intervals. In this way, the criteria of parameter selection for system application are given. In particular, the effect of Gaussian white noise on the dynamic behavior of memristive CNN chaotic system is studied. The hardware circuit design and characteristic analysis of memristive cellular neural network are completed by the circuit simulation software, and the physical realizability of chaotic characteristics of the memristive cellular neural network model is verified. Furthermore, a secure communication application example based on the hyperchaotic system is given.

Symmetric coexisting attractors and extreme multistability in chaotic system

In this paper, a new four-dimensional (4D) chaotic system with two cubic nonlinear terms is proposed. The most striking feature is that the new system can exhibit completely symmetric coexisting bifurcation behaviors and four symmetric coexisting attractors with the same Lyapunov exponents in all parameter ranges of the system when taking different initial states. Interestingly, these symmetric coexisting attractors can be considered as unusual symmetrical rotational coexisting attractors, which is a very fascinating phenomenon. Furthermore, by using a memristor to replace the coupling resistor of the new system, an interesting 4D memristive hyperchaotic system with one unstable origin is constructed. Of particular surprise is that it can exhibit four groups of extreme multistability phenomenon of infinitely many coexisting attractors of symmetric distribution about the origin. By using phase portraits, Lyapunov exponent spectra, and coexisting bifurcation diagrams, the dynamics of the two systems are fully analyzed and investigated. Finally, the electronic circuit model of the new system is designed for verifying the feasibility of the new chaotic system.

Chaos-Based Engineering Applications with a 6D Memristive Multistable Hyperchaotic System and a 2D SF-SIMM Hyperchaotic Map

In recent years, the research of chaos theory has developed from simple cognition and analysis to practical engineering application. In particular, hyperchaotic systems with more complex and changeable chaotic characteristics are more sensitive and unpredictable, so they are widely used in more fields. In this paper, two important engineering applications based on hyperchaos pseudorandom number generator (PRNG) and image encryption are studied. Firstly, the coupling 6D memristive hyperchaotic system and a 2D SF-SIMM discrete hyperchaotic mapping are used as the double entropy source structure. The double entropy source structure can realize a new PRNG that meets the security requirements, which can pass the NIST statistical test when the XOR postprocessing method is used. Secondly, based on the double entropy source structure, a new image encryption algorithm is proposed. The algorithm uses the diffusion-scrambling-diffusion encryption scheme to realize the conversion from the original plaintext image to the ciphertext image. Finally, we analyze the security of the proposed PRNG and image encryption mechanism, respectively. The results show that the proposed PRNG has good statistical output characteristics and the proposed image encryption scheme has high security, so they can be effectively applied in the field of information security and encryption system.

Exploiting preprocessing-permutation–diffusion strategy for secure image cipher based on 3D Latin cube and memristive hyperchaotic system

In this paper, an effective image encryption algorithm based on 3D Latin cube and memristive hyperchaotic system is proposed. The architecture of preprocessing, permutation and diffusion is utilized. The original image is updated for the first time by the preprocessing process to modify statistical distribution of image pixels, which includes random data embedding and alphabetic XOR operation (AXO). Subsequently, the resulting image is converted to a 3D bit matrix, permutation based on 3D Latin cube (P3DL) and diffusion based on 3D Latin cube (D3DL) are successively manipulated on it to obtain the final cipher image, such that each bit element of plain image may move to any position across the bit plane, and the general transformation of matrix dimensions from permutation to diffusion is also unnecessary. Additionally, the adoption of preprocessing operation makes the permutation easy to resist attacks against special images. Moreover, random data used in preprocessing and 3D Latin cubes utilized in P3DL and D3DL are controlled by a 4D memristive hyperchaotic system, its initial values are computed by information entropy of plain image, which makes the chosen-plaintext and known-plaintext attacks invulnerable. Simulation results and performance analyses verify the effectiveness and security of the proposed image encryption scheme.