Memristive Chaotic System Research Articles

Coexistence of hidden attractors in memristive chaotic system

In this paper, a charge controlled memristor model is introduced into the Sprott-A system equation to construct a new memristor chaotic system and the calculation of this new system satisfies the characteristics of no equilibrium points. The periodic function is added to the new constructed memristor chaotic system, and the coexistence of attractors in memristor chaotic system without equilibrium points is obtained by adjusting the control parameters. Through different analytical methods to explore the characteristics of the new system. The dynamic behaviors of the system before and after the periodic transformation are compared and analyzed. In the end, DSP simulation is used to verify the feasibility of the theoretical model. The coexistence of attractors in memristor chaotic systems can improve the flexibility and security of chaotic encryption systems. Further research on this kind of phenomena can meet the needs of higher encryption.

Design and FPGA realization of memristive multibutterfly chaotic system featuring coexisting attractors and complex multistability behavior

Design and FPGA realization of memristive multibutterfly chaotic system featuring coexisting attractors and complex multistability behavior

Block-based color image encryption algorithm by a novel memristor chaotic system and new RNA computation

The security of images is closely related to the protection of information privacy. We proposed a novel 5D memory resistive chaotic system (5D-MRCS), which exhibits good chaotic characteristics. Therefore, we employed it to design an image encryption algorithm aimed at ensuring secure image transmission. To further enhance the complexity of the algorithm and obtain more chaotic sequences, we combine the 5D-MRCS with the Hodgkin-Huxley (HH) model and use this combination in algorithm design. Initially, we combine the plain image with the hash function SHA-384 to devise and generate the secret key. Subsequently, the algorithm determines whether to pad the plain image based on different block size requirements. Then, we use multiple chaotic sequences generated by the 5D-MRCS and HH model to perform the global image permutation operation. Our designed permutation algorithm includes two parts: Block-based permutation and a new pixel-level permutation. Next, the scrambled image undergoes block-based random RNA diffusion, incorporating two newly proposed methods in the RNA operations, ultimately resulting in the ciphertext image. The algorithm’s NPCR, UACI, information entropy, and other security performance metrics are very close to the ideal values, and it possess characteristics such as resistance to differential, cutting, chosen plaintext, and noise attacks. Compared with other algorithms, it still has some advantages across multiple images and demonstrates excellent image encryption performance.

Sliding-mode-based preassigned-time control of a class of memristor chaotic systems

Abstract This paper addresses the preassigned-time chaos control problem of memristor chaotic systems with time delays. Since the introduction of memristor, the presented models are nonlinear systems with chaotic dynamics. First, the TS fuzzy method is adopted to describe the chaotic systems. Then, a sliding-model-based control approach is proposed to achieve the preassigned-time stabilization of the presented models, where the upper bound of stabilization time can be arbitrarily specified in advance. Finally, simulation results demonstrate the validity of presented control approach and theoretic results.

Memristor-coupled cubic hyperchaotic system, feedback synchronization and its application in image encryption

Discrete memristive chaotic systems play a crucial role in information security, and chaotic synchronization form the bedrock of secure and confidential communication. To enhance the chaotic complexity of the Cubic map, we introduce a memristor-coupled Cubic hyperchaotic system by integrating a discrete absolute memristor model with the Cubic map. The dynamics are thoroughly investigated through attractor phase diagrams, bifurcation diagrams, SE complexity analysis, and diagrams illustrating the distribution of dynamic behaviors. Furthermore, we establish methods for chaos control and nonlinear feedback synchronization for the memristive Cubic map. Leveraging this feedback synchronization, we achieve encrypted transmission of digital images. Simulation results validate the feasibility and robust security of the proposed encrypted transmission scheme.

An image encryption scheme based on an improved memristive neuron chaotic system

With fast-developing Internet and communication, the security transmission of image in network has become a research highlight. So far, researchers have designed a lot of image encryption methods based on chaotic models, some of them are not secure enough. To enhance security of image transmission on the network, in this paper, an image encryption method is developed from a 3D memeristive FitzHugh-Nagumo (FHN) neuron. First, a 3D memeristive FHN model is obtained by connecting a memeristor into a 2D FHN model, and dynamics for 3D FHN model are estimated by applying phase diagrams, bifurcation and Lyapunov exponent. Then, an image encryption algorithm is proposed by using this 3D model. Finally, security of encryption algorithm is estimated. Simulation results confirm the effectiveness of encryption scheme.

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.

Design of chaotic circuit based on Knowm memristor

AbstractMost previous works in the field of nonlinear memristive chaotic systems mainly focus on non‐material memristor while seldom on material memristor. In this letter, the model and the corresponding parameter identification of the Knowm memristor is presented. The chaotic circuit based on the Knowm memristor is designed. Equilibrium points and stability of this Knowm‐memristor‐based chaotic system is analyzed. Nonlinear dynamic behavior is presented by the bifurcation diagram and Lyapunov exponents. Finally, the hardware circuit of this Knowm‐memristor‐based chaotic system is designed and the experimental results are presented for confirmation.

Research on Variable Parameter Color Image Encryption Based on Five-Dimensional Tri-Valued Memristor Chaotic System.

To construct a chaotic system with complex characteristics and to improve the security of image data, a five-dimensional tri-valued memristor chaotic system with high complexity is innovatively constructed. Firstly, a pressure-controlled tri-valued memristor on Liu's pseudo-four-wing chaotic system is introduced. Through analytical methods, such as Lyapunov exponential map, bifurcation map and attractor phase diagram, it is demonstrated that the new system has rich dynamical behaviors with periodic limit rings varying with the coupling parameter of the system, variable airfoil phenomenon as well as transient chaotic phenomenon of chaos-periodic depending on the system parameter and chaos-quasi-periodic depending on the memristor parameter. The system is simulated with dynamic circuits based on Simulink. Secondly, the differently structured synchronous controls of chaotic systems are realized using a nonlinear feedback control method. Finally, based on the newly constructed five-dimensional chaotic system, a variable parameter color image encryption scheme is proposed to iteratively generate varying chaotic pseudo-random sequences by varying the system parameters, which will be used for repetition-free disambiguation, additive modulo left-shift diffusion and DNA encryption for the three components of RGB of the color image after chunking. The simulation results are analyzed by histogram, information entropy, adjacent pixel correlation, etc., and the images are tested using differential attack, noise attack and geometric attack, as well as analyzing the PSNR and SSIM of the decrypted image quality. The results show that the encryption method has a certain degree of security and can be applied to medical, military and financial fields with more complex environmental requirements.

A memristive chaotic system with two dimensional offset boosting and extreme multistability

Due to its unique nonlinearity and memory characteristics, memristor is considered one of the most promising partners for designing chaotic systems. In this paper, a memristor is introduced into a nonlinear system to produce complex dynamical behaviors. Symmetric extremely multistability induced by the initial condition of the memristor is observed in the asymmetric system. Attractors are arranged in the phase space by two independent offset boosters, strength cancellation gives birth to various offset boosting patterns. The effective action of the offset controller is reflected in the linear growth of the mean values and the linear shift of the signal diagrams. Moreover, the circuit implementation based on Multisim demonstrates consistency with numerical simulations and theoretical analyses. Finally, the Pseudorandom Number Generator (PRNG), tested through NIST, is developed to validate its high performance in engineering applications.

Design and analysis of image encryption based on memristor chaotic systems with hidden attractors

Chaotic systems with hidden attractors are important research hotspots in nonlinear science. In recent years, continuous chaotic systems with special equilibrium points have been widely studied, especially continuous chaotic systems without equilibrium points. A four-dimensional chaotic system devoid of equilibrium point is proposed by using a composite cosine piecewise-linear (COS-PWL)function and a memristor model based on the modified Sprott-C system. The dynamical behaviors of the new system are studied through numerical analysis methods. The results reveal it is extremely sensitive to control parameters as well as initial conditions, which make it particularly suitable for application to image encryption algorithms. In light of these findings, a novel image encryption algorithm is introduced. This algorithm integrates the new four-dimensional chaotic system with ribonucleic acid (RNA) coding technology. Furthermore, the simulation results and security analyses validate the rationality of the encryption mechanism and the robustness of the encryption security of the proposed image encryption algorithm.

Dynamics modeling of a memristor-based Rucklidge chaotic system: Multistability, offset boosting control and FPGA implementation

The complex dynamics greatly contributes to the application of chaos, especially the memristor chaotic systems that have emerged very recently. In this paper, a novel four-dimensional continuous chaotic system is developed by introducing a generalized memristor model into the classical Rucklidge system, and the rich dynamical traits are confirmed by theories and numerical simulations. System Hamilton energy is deduced and analyzed to expose the underlying energy evolution and chaos mechanism. And then, realizing the offset boosting control of the system promotes its engineering applications. Numerical simulations verify that the offset boosting controller can directly change the polarity of the chaotic signal. Specifically, bifurcation diagram, Lyapunov spectra, system complexity evolution diagram and dynamic evolution map are adopted to expound the rich dynamics. Meanwhile, the extreme multi-stability with various initial values resulting in an infinite number of coexisting attractors is also revealed. Finally, the proposed attractor is implemented using the Field Programmable Gate Array (FPGA) platform and building analog circuit based on Multisim. Among which, the former is potentially used to design the Pseudo-random signal generator in information encryption, while the latter is for verifying the existence of the proposed chaotic system.

Adaptive control for memristive system via compensatory controller and Chebyshev neural network

In this paper, based on linear matrix inequality technique, a simple controller and a compensatory controller are designed. It can track arbitrary fixed points and any periodic orbits. In addition, a synchronization control method via Chebyshev neural network with external disturbances is proposed. An adaptive controller is given. The Chebyshev neural network is used to approximate the uncertain nonlinear function and the adaptive law is used to adjust the corresponding parameters in the system. Taking a 4D memristive chaotic system as examples, the results are in consistent with the simulations. From a framework and control theoretical point of view, the proposed synchronization approach via compensation controller and Chebyshev neural network is firstly presented. From an application point of view, the proposed scheme can simplify the complexity of controller design. It is promising in many applications for mem-systems as secure communications and neural networks.

Integrated circuit design of a discrete memristive chaotic system optimized by the fixed-point specific processor with acceleration instructions

Integrated circuit design of a discrete memristive chaotic system optimized by the fixed-point specific processor with acceleration instructions

Design of Pseudorandom Signal Generator Based on a Dual Memristor Chaotic System

This paper constructs a pseudo-random signal generator based on a dual memristor chaotic system. Firstly, the chaotic characteristics of the dual memristor chaotic system were explored through theoretical analysis and MATLAB numerical simulation, and a MULTISIM simulation circuit for the dual memristor chaotic system was constructed. Then, based on the threshold decision quantization method, a pseudorandom signal generator quantization circuit is formed by connecting an inverter amplifier and a hysteresis comparator on the output side of the analog circuit. Finally, the randomness of the pseudorandom sequence is discussed by NIST test and correlation analysis. The analysis results show that the pseudorandom sequence generated by the pseudo-random signal generator based on the dual memristor chaotic system exhibits good randomness.

Analysis of the Dynamics of a Cubic Nonlinear Five-Dimensional Memristive Chaotic System and the Study of Reduced-Dimensional Synchronous Masking

To improve the complexity of the chaotic system and achieve the effective transmission of image information, in this paper, a five-dimensional memristive chaotic system with cubic nonlinear terms is constructed, which has four pairs of symmetric coordinates. First, the cubic nonlinear memristive chaotic system is analyzed using the Lyapunov exponential map, bifurcation map, and attractor phase diagram. The experimental results show that under four pairs of symmetric coordinates, the system exists not only parameter-dependent symmetric rotational coexisting attractor and transient chaotic phenomena but also exists super-multistationary with alternating chaotic cycles dependent on the initial value of the memristor. Then, it is proposed to add a constant term to the linear state variable to explore the effect of the offset increment of the linear state variable on the system in four pairs of symmetric coordinates, while circuit simulation of the five-dimensional chaotic system is carried out using Simulink to verify its existence and realisability. Finally, the synchronization of the dimensionality reduction system and the confidential transmission of the image are achieved, using the control voltage of the system to replace the internal state variables of the memristor to achieve the one-dimensional reduction process, and an adaptive synchronization controller is designed to synchronize the system before and after the dimensionality reduction. Based on the above, an image to be transmitted is modulated into a one-dimensional array and then subjected to the fractional and cyclic operations and combined with the linear encryption and decryption functions and the chaotic masking technique, the simple encryption and decryption of the image processes are realized.

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.

Complexity enhancement and grid basin of attraction in a locally active memristor-based multi-cavity map

The complexity of memristive chaotic systems determines whether it is suitable for applications in different subjects. To enhance complexity both in performance and diversity, this article first proposes a discrete model of locally active memristor (LAM) and conceives a three-dimensional memristive multi-cavity map by coupling LAM with the existing sine and cosine modulation (SCM) map. This map is named LAM-SCM map and has numerous independent fixed points with different stabilities. Numerical simulations reveal the memristive parameters-relied lossless displacement and self-shift of multi-cavity attractors, indicating the dynamical effects of LAM on the existing SCM map. The initial-relied dynamics distributions are disclosed by grid basins of attraction, showing the emergence of initial-boosting coexistence. Besides, the performance comparisons verify the superiority of LAM-SCM map over the existing SCM map. Finally, a hardware platform has been developed on FPGA to implement the LAM-SCM map and the captured attractors validate the numerical results. On this basis, we devise a 32-bit pseudorandom number generator (PRNG) based on chaos and implement it on the FPGA-based hardware platform to obtain high-speed and reconfigurable pseudorandom numbers. The results show that the proposed map has enhanced chaos complexity and rich dynamics diversity, which ensures the availability of hardware PRNG.

A tri-valued memristive chaotic system with hidden attractors and its image encryption application

A tri-valued memristive chaotic system with hidden attractors and its image encryption application

Adaptive Intermittent Stabilization of Memristive Chaotic System via T-S Fuzzy Model

Adaptive Intermittent Stabilization of Memristive Chaotic System via T-S Fuzzy Model