From Memristor-Modeled Jerk System to the Nonlinear Systems with Memristor

Wu, Xiaofeng; He, Shaobo; Tan, Weijie; Wang, Huihai

doi:10.3390/sym14040659

Cited by 8 publications

(3 citation statements)

References 43 publications

(40 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the discrete memristor, it should have the three fingerprints when the input of the discrete memristor contains bipolar periodic signals. For the function

, there are many different choices, including piecewise nonlinearity, linear nonlinearity, absolute value, linear function, sine function, and square function [ 44 ]. In this manuscript, we use the idea of memristor models including HP memristors (linear function) and absolute function, to show the effectiveness of the proposed methods.…”

Section: Preliminariesmentioning

confidence: 99%

Discrete Memristor and Discrete Memristive Systems

He,

Zhan,

Wang

et al. 2022

Entropy

Self Cite

View full text Add to dashboard Cite

In this paper, we investigate the mathematical models of discrete memristors based on Caputo fractional difference and G–L fractional difference. Specifically, the integer-order discrete memristor is a special model of those two cases. The “∞”-type hysteresis loop curves are observed when input is the bipolar periodic signal. Meanwhile, numerical analysis results show that the area of hysteresis decreases with the increase of frequency of input signal and the decrease of derivative order. Moreover, the memory effect, characteristics and physical realization of the discrete memristors are discussed, and a discrete memristor with short memory effects is designed. Furthermore, discrete memristive systems are designed by introducing the fractional-order discrete memristor and integer-order discrete memristor to the Sine map. Chaos is found in the systems, and complexity of the systems is controlled by the parameter of the memristor. Finally, FPGA digital circuit implementation is carried out for the integer-order and fractional-order discrete memristor and discrete memristive systems, which shows the potential application value of the discrete memristor in the engineering application field.

show abstract

“…For the discrete memristor, it should have the three fingerprints when the input of the discrete memristor contains bipolar periodic signals. For the function

Section: Preliminariesmentioning

confidence: 99%

Discrete Memristor and Discrete Memristive Systems

He,

Zhan,

Wang

et al. 2022

Entropy

Self Cite

View full text Add to dashboard Cite

show abstract

“…From then on, research on memristors has attracted a huge amount of attention in industry and academia. Their natural nonlinear and non-volatile characteristics give memristors great potential for data storage and computation [3,4], artificial neural networks [5][6][7], nonlinear circuits [8][9][10], secure communication [11], image encryption [12][13][14], and other fields.…”

Section: Introductionmentioning

confidence: 99%

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

Wang

Zhang

et al. 2023

Symmetry

View full text Add to dashboard Cite

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.

show abstract

“…Due to the rapid advancement of chaos theory, chaotic and hyperchaotic systems are applicable in several engineering branches such as memristive circuits [1][2][3][4], chemical oscillators [5][6][7], information sensing systems [8][9][10], lasers [11,12], and communication systems [13][14][15][16]. Xiu et al [17] designed a 5-D hyperchaotic system with hardware circuit design developed from a memristive cellular neural network (CNN) and applied it to build a secure communication system.…”

Section: Introductionmentioning

confidence: 99%

A New Hyperchaotic Two‐Scroll System: Bifurcation Study, Multistability, Circuit Simulation, and FPGA Realization

Vaidyanathan

Sambas

Tlelo‐Cuautle

et al. 2022

Discrete Dynamics in Nature and Society

View full text Add to dashboard Cite

With the swift advancement of chaos theory, the modeling, chaotic oscillations, and engineering applications of chaotic and hyperchaotic systems are important topics in research. In this research paper, we elucidate our findings of a new four-dimensional two-scroll hyperchaotic system having only two quadratic nonlinearities and carry out a detailed bifurcation study of the proposed dynamical model. Also, an electronic circuit has been constructed for the new system using MultiSim (Version 14). The implementation of the new 4-D hyperchaotic system in a field-programmable gate array (FPGA) is performed herein by applying two numerical methods, viz. Forward Euler Method and Trapezoidal Method. The experimental results show a good match with the simulated hyperchaotic attractors. We also provide details of the hardware resources used for an FPGA Basys 3 Xilinx Artix-7 XC7A35T-ICPG236C.

show abstract

From Memristor-Modeled Jerk System to the Nonlinear Systems with Memristor

Cited by 8 publications

References 43 publications

Discrete Memristor and Discrete Memristive Systems

Discrete Memristor and Discrete Memristive Systems

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

A New Hyperchaotic Two‐Scroll System: Bifurcation Study, Multistability, Circuit Simulation, and FPGA Realization

Contact Info

Product

Resources

About