Memristive Chaotic Research Articles

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.

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

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

Constructing a Memristive Chaotic Oscillator With Two-Dimensional Offset Boosting

Constructing a Memristive Chaotic Oscillator With Two-Dimensional Offset Boosting

A Conservative Memristive Chaotic System with Extreme Multistability and Its Application in Image Encryption.

In this work, a novel conservative memristive chaotic system is constructed based on a smooth memristor. In addition to generating multiple types of quasi-periodic trajectories within a small range of a single parameter, the amplitude of the system can be controlled by changing the initial values. Moreover, the proposed system exhibits nonlinear dynamic characteristics, involving extreme multistability behavior of isomorphic and isomeric attractors. Finally, the proposed system is implemented using STMicroelectronics 32 and applied to image encryption. The excellent encryption performance of the conservative chaotic system is proven by an average correlation coefficient of 0.0083 and an information entropy of 7.9993, which provides a reference for further research on conservative memristive chaotic systems in the field of image encryption.

A New Secure Communications Scheme Based on a Synchronisation of Hybrid Chaotic System

This paper presents a novel approach for secure communication utilizing a chaotic hybrid optical bistable system and chaotic modulation. The proposed crypto system encrypts the message at the transmitter using the chaotic hybrid optical bistable system with decorrelation operation to improve the chaotic sequence's performance. The encoded message is then injected into the dynamics of the chaotic memristor system. At the receiver, the synchronization of the two chaotic systems with passive control and predictive control allows for the recovery of the message through chaotic demodulation. The effectiveness of this approach is demonstrated through numerical simulation using medical images.

Characterization of second-order chaotic circuits with heterogeneous memristors

Abstract 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.

A Novel Memristive Chaotic System with Hidden Attractors and a Line of Equilibria

A Novel Memristive Chaotic System with Hidden Attractors and a Line of Equilibria

Multiscroll Chaos and Extreme Multistability of Memristive Chaotic System with Application to Image Encryption

Multiscroll Chaos and Extreme Multistability of Memristive Chaotic System with Application to Image Encryption

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.

Dynamics and Circuit Implementation of a 4D Memristive Chaotic System with Extreme Multistability

In this paper, a four-dimensional chaotic system based on a flux-controlled memristor with cosine function is constructed. It has infinitely many equilibria. By changing the initial values [Formula: see text], [Formula: see text] and [Formula: see text] of the system and keeping the parameters constant, we obtained the distribution of infinitely many single-wing and double-wing attractors along the [Formula: see text]-coordinate, which verifies the initial-offset boosting behavior of the system. Then the complex dynamical behavior of the system is studied in detail through the phase portraits of coexisting attractors, the average value of state variables, Lyapunov exponent spectrum, bifurcation diagram, attraction basin and the complexity of spectral entropy (SE). In addition, the simulation of the Multisim circuit is also carried out, and the results of numerical simulation and analog circuit simulation are consistent. Finally, the chaotic sequence generated by the system is applied to image encryption, and according to the performance analysis, the proposed chaotic system has good security performance.

A New Pelican Optimization Algorithm for the Parameter Identification of Memristive Chaotic System

A memristor is a kind of nonlinear electronic component. Parameter identification for memristive chaotic systems is a multi-dimensional variable optimization problem. It is one of the key issues in chaotic control and synchronization. To identify the unknown parameters accurately and quickly, we introduce, in this paper, a modified Pelican Optimization Algorithm (POA) called the fractional-order chaotic Pareto Pelican Optimization Algorithm (FPPOA). First, the pelican population’s diversity is augmented with the integration of a fractional chaotic sequence. Next, the utilization of the Pareto distribution is incorporated to alter the hunting strategy of pelicans in the POA. These measures are effective in hastening the speed of finding an optimal solution and circumventing local optimization issues. Thirdly, the FPPOA is used to determine the values of the parameters of the simplest memristive chaotic system, which has a property of conditional symmetry. The proposed algorithm was evaluated during simulations, where it was utilized to solve six objective functions of varying unimodal and multimodal types. The performance of the FPPOA exceeds three traditional swarm intelligence optimization algorithms. In the parameter identification experiment, the results for the parameters with the FPPOA had error rates all within a 1% range. Extensive testing shows that our new strategy has a faster rate of convergence and better optimization performance than some other traditional swarm algorithms.

An Encryption Application and FPGA Realization of a Fractional Memristive Chaotic System

The work in this paper extends a memristive chaotic system with transcendental nonlinearities to the fractional-order domain. The extended system’s chaotic properties were validated through bifurcation analysis and spectral entropy. The presented system was employed in the substitution stage of an image encryption algorithm, including a generalized Arnold map for the permutation. The encryption scheme demonstrated its efficiency through statistical tests, key sensitivity analysis and resistance to brute force and differential attacks. The fractional-order memristive system includes a reconfigurable coordinate rotation digital computer (CORDIC) and Grünwald–Letnikov (GL) architectures, which are essential for trigonometric and hyperbolic functions and fractional-order operator implementations, respectively. The proposed system was implemented on the Artix-7 FPGA board, achieving a throughput of 0.396 Gbit/s.

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.

Analysis and Realization of New Memristive Chaotic System with Line Equilibria and Coexisting Attractors

Analysis and Realization of New Memristive Chaotic System with Line Equilibria and Coexisting Attractors

K-Means Clustering Algorithm Based on Memristive Chaotic System and Sparrow Search Algorithm

With the advent of the big data era, it is vital to explore the information involved in this type of data. With the continuous development of higher education, the K-means clustering algorithm is widely used to analyze students’ academic data. However, a significant drawback of this method is that it is seriously affected by initial centroids of clustering and easily falls into local optima. Motivated by the fact that the chaos and swarm intelligence algorithm are frequently combined, we propose an approach for data clustering by Memristive Chaotic Sparrow Search Algorithm (MCSSA) in this paper. First, we introduce a memristive chaotic system, which has a property of conditional symmetry. We use the sequences generated by the memristive chaotic system to initialize the location of the sparrows. Then, MCSSA is applied before K-means for finding the optimal locations in the search space. Those locations are used as initial cluster centroids for the K-means algorithm to find final data clusters. Finally, the improved clustering algorithm is applied to the analysis of college students’ academic data, demonstrating the value and viability of the approach suggested in this paper. Through empirical research, it is also confirmed that this method can be promoted and applied.

A new 4D Memristor chaotic system: Analysis and implementation

In this paper, a new chaotic memristor system is developed based on a well-known nonlinear circuit. By replacing the nonlinear positive conductance of Shinriki's circuit with a memristor emulator, the new simple chaotic circuit can reduce the number of active elements and reduce power consumption. An analysis of equilibria and stability, dissipative properties, Lyapunov exponents, Kaplan-Yorke dimensions, and bifurcation diagrams is presented as well as numerical simulation of the new memristor chaotic system. As a final step, the electronic circuit is designed using Multisim software, which is complemented by a physical realization to demonstrate the feasibility of the chaotic system.

Hyperchaotic circuit design based on memristor and its application in image encryption

The active-circuit simulation of magnetron memristors model and sinusoidal functions are introduced into a simple third-order memristor chaotic system to obtain a self-replicating chaotic system based on the memristor. The most remarkable feature is the existence of state transfer in this system, which has infinite line equilibria and exhibits extreme multistability with the coexistence of an infinite number of attractors. The system is a chaotic system with a wide range of parameters, and there is a transfer from periodic to chaotic to hyperchaotic states in a specific parameter range. The experimental simulation circuit was not only developed based on the circuit simulation software Multisim, but also the actual digital circuit of the system was implemented by field programmable gate array (FPGA). The final experimental results were consistent with the numerical simulation, which proved that the constructed system was feasible. Finally, an image encryption algorithm is designed in combination with DNA algorithm, so that the new system chaotic sequence is used to encrypt images, focusing on the analysis of encryption histogram, adjacent pixel correlation. The results show that the new memristor system is very sensitive to both chaotic keys and plaintexts, the key space is large, therefore the proposed chaotic memristor system has high security performance when applied to image encryption.

Extreme Multistability Dynamics in a New 3d Memristive Chaotic System with Circuit Realisation

Extreme Multistability Dynamics in a New 3d Memristive Chaotic System with Circuit Realisation

High-Security Image Encryption Based on a Novel Simple Fractional-Order Memristive Chaotic System with a Single Unstable Equilibrium Point

Fractional-order chaotic systems have more complex dynamics than integer-order chaotic systems. Thus, investigating fractional chaotic systems for the creation of image cryptosystems has been popular recently. In this article, a fractional-order memristor has been developed, tested, numerically analyzed, electronically realized, and digitally implemented. Consequently, a novel simple three-dimensional (3D) fractional-order memristive chaotic system with a single unstable equilibrium point is proposed based on this memristor. This fractional-order memristor is connected in parallel with a parallel capacitor and inductor for constructing the novel fractional-order memristive chaotic system. The system’s nonlinear dynamic characteristics have been studied both analytically and numerically. To demonstrate the chaos behavior in this new system, various methods such as equilibrium points, phase portraits of chaotic attractor, bifurcation diagrams, and Lyapunov exponent are investigated. Furthermore, the proposed fractional-order memristive chaotic system was implemented using a microcontroller (Arduino Due) to demonstrate its digital applicability in real-world applications. Then, in the application field of these systems, based on the chaotic behavior of the memristive model, an encryption approach is applied for grayscale original image encryption. To increase the encryption algorithm pirate anti-attack robustness, every pixel value is included in the secret key. The state variable’s initial conditions, the parameters, and the fractional-order derivative values of the memristive chaotic system are used for contracting the keyspace of that applied cryptosystem. In order to prove the security strength of the employed encryption approach, the cryptanalysis metric tests are shown in detail through histogram analysis, keyspace analysis, key sensitivity, correlation coefficients, entropy analysis, time efficiency analysis, and comparisons with the same fieldwork. Finally, images with different sizes have been encrypted and decrypted, in order to verify the capability of the employed encryption approach for encrypting different sizes of images. The common cryptanalysis metrics values are obtained as keyspace = 2648, NPCR = 0.99866, UACI = 0.49963, H(s) = 7.9993, and time efficiency = 0.3 s. The obtained numerical simulation results and the security metrics investigations demonstrate the accuracy, high-level security, and time efficiency of the used cryptosystem which exhibits high robustness against different types of pirate attacks.

A New Memristive Chaotic System with a Plane and Two Lines of Equilibria

A new 4D memristive chaotic system with an infinite number of equilibria is proposed via exhaustive computer search. Interestingly, such a new memristive system has a plane of equilibria and two other lines of equilibria. Lyapunov exponent and bifurcation analysis show that this system has chaotic solutions with coexisting attractors. The basins of attraction of the coexisting attractors show chaos, stable fixed-points, and unbounded solutions. Furthermore, the 2D parameter space of the system is explored to find the optimum values of the parameters using the ALO (Ant Lion Optimizer) optimization algorithm.