Complex Dynamics of a Novel Chaotic System Based on an Active Memristor

On the basis of the bistable bi-local active memristor (BBAM), an active memristor (AM) and its emulator were designed, and the characteristic fingerprints of the memristor were found under the applied periodic voltage. A memristor-based chaotic circuit was constructed, whose corresponding dynamics system was described by the 4-D autonomous differential equations. Complex dynamics behaviors, including chaos, transient chaos, heterogeneous coexisting attractors, and state-switches of the system were analyzed and explored by using Lyapunov exponents, bifurcation diagrams, phase diagrams, and Poincaré mapping, among others. In particular, a novel exotic chaotic attractor of the system was observed, as well as the singular state-switching between point attractors and chaotic attractors. The results of the theoretical analysis were verified by both circuit experiments and digital signal processing (DSP) technology.

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Extreme Multistability and Complex Dynamics of a Memristor-Based Chaotic System

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127420300190 ◽

2020 ◽

Vol 30 (08) ◽

pp. 2030019

Author(s):

Hui Chang ◽

Yuxia Li ◽

Guanrong Chen ◽

Fang Yuan

Keyword(s):

Complex Dynamics ◽

Hysteresis Loops ◽

Digital Signal ◽

Phase Portraits ◽

Transient Chaos ◽

Bifurcation Diagrams ◽

Extreme Multistability ◽

Memristive System ◽

Autonomous Differential Equations ◽

Pinched Hysteresis

A memristor with coexisting pinched hysteresis loops and twin local activity domains is presented and analyzed, with an emulator being designed and applied to the classic Chua’s circuit to replace the diode. The memristive system is modeled with four coupled first-order autonomous differential equations, which has three equilibria determined by three static equilibria of the memristor but not controlled by the system parameters. The complex dynamics of the system are analyzed by using compound coexisting bifurcation diagrams, Lyapunov exponent spectra and phase portraits, including point attractors, limit cycles, symmetrical chaotic attractors and their blasting, extreme multistability, state-switching without parameter, and transient chaos. Of particular surprise is that the extreme multistability of the system is hidden and symmetrically distributed. It is found that the existence of transient chaos in the specified parameter domain is determined by using bifurcation diagrams within different time durations and Lyapunov exponents with chaotic sequences. Finally, the symmetrical chaotic attractor and the system blasting are verified by digital signal processing experiments, which are consistent with the numerical analysis.

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A Novel Memcapacitor and Its Application in a Chaotic Circuit

10.21203/rs.3.rs-221899/v1 ◽

2021 ◽

Author(s):

Mei Guo ◽

Ran Yang ◽

Meng Zhang ◽

Renyuan Liu ◽

Yongliang Zhu ◽

...

Keyword(s):

Steady State ◽

Transient Chaos ◽

Bifurcation Diagrams ◽

Chaotic Circuit ◽

Coexisting Attractors ◽

Dynamic Behaviors ◽

Burst Period ◽

The Stability ◽

Fifth Order ◽

Stable Points

Abstract In this paper, a novel memcapacitor is designed by SBT memristor and two capacitors. A fifth-order memcapacitor and memristor chaotic circuit is proposed. The stability of the equilibrium point of the system is analyzed theoretically. Lyapunov exponents spectra, bifurcation diagrams, poincaré maps and phase diagrams are used to analyze the dynamic behaviors of the system. The results show that under different initial values and parameters, the system produces rich dynamic behaviors such as stable points, limit cycles, chaos, and so on. Specially, coexisting attractors, transient chaos, and steady-state chaos accompanied by burst period phenomenon are also produced in the system. The proposed memcapacitor-based circuit expands the research methods of memcapacitor for application in chaoticcircuits.

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Coexisting Attractors and Multistability in a Simple Memristive Wien-Bridge Chaotic Circuit

Entropy ◽

10.3390/e21070678 ◽

2019 ◽

Vol 21 (7) ◽

pp. 678 ◽

Cited By ~ 13

Author(s):

Yixuan Song ◽

Fang Yuan ◽

Yuxia Li

Keyword(s):

Chaotic System ◽

Analog Circuit ◽

Random Sequence ◽

Mathematical Expression ◽

Digital Signal ◽

Approximate Entropy ◽

Chaotic Circuit ◽

Coexisting Attractors ◽

Key Space ◽

Sequence Generator

In this paper, a new voltage-controlled memristor is presented. The mathematical expression of this memristor has an absolute value term, so it is called an absolute voltage-controlled memristor. The proposed memristor is locally active, which is proved by its DC V–I (Voltage–Current) plot. A simple three-order Wien-bridge chaotic circuit without inductor is constructed on the basis of the presented memristor. The dynamical behaviors of the simple chaotic system are analyzed in this paper. The main properties of this system are coexisting attractors and multistability. Furthermore, an analog circuit of this chaotic system is realized by the Multisim software. The multistability of the proposed system can enlarge the key space in encryption, which makes the encryption effect better. Therefore, the proposed chaotic system can be used as a pseudo-random sequence generator to provide key sequences for digital encryption systems. Thus, the chaotic system is discretized and implemented by Digital Signal Processing (DSP) technology. The National Institute of Standards and Technology (NIST) test and Approximate Entropy analysis of the proposed chaotic system are conducted in this paper.

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Symmetric Coexisting Attractors in a Novel Memristors-Based Chuas Chaotic System

Journal of Circuits System and Computers ◽

10.1142/s0218126622501201 ◽

2021 ◽

Author(s):

Shaohui Yan ◽

Zhenlong Song ◽

Wanlin Shi

Keyword(s):

Lyapunov Exponent ◽

Chaotic System ◽

Analog Circuits ◽

Complex Dynamics ◽

Chaotic Attractors ◽

Coexisting Attractors ◽

Initial Value ◽

Field Programmable ◽

A Charge ◽

Lyapunov Exponent Spectrum

This paper introduces a charge-controlled memristor based on the classical Chuas circuit. It also designs a novel four-dimensional chaotic system and investigates its complex dynamics, including phase portrait, Lyapunov exponent spectrum, bifurcation diagram, equilibrium point, dissipation and stability. The system appears as single-wing, double-wings chaotic attractors and the Lyapunov exponent spectrum of the system is symmetric with respect to the initial value. In addition, symmetric and asymmetric coexisting attractors are generated by changing the initial value and parameters. The findings indicate that the circuit system is equipped with excellent multi-stability. Finally, the circuit is implemented in Field Programmable Gate Array (FPGA) and analog circuits.

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A Simple Parallel Chaotic Circuit Based on Memristor

Entropy ◽

10.3390/e23060719 ◽

2021 ◽

Vol 23 (6) ◽

pp. 719

Author(s):

Xiefu Zhang ◽

Zean Tian ◽

Jian Li ◽

Zhongwei Cui

Keyword(s):

Time Domain ◽

Sample Entropy ◽

Chaotic Attractors ◽

Largest Lyapunov Exponent ◽

Spectral Entropy ◽

Chaotic Circuit ◽

Coexisting Attractors ◽

Periodic Attractors ◽

Dynamic Map ◽

Lyapunov Exponent Spectrum

This paper reports a simple parallel chaotic circuit with only four circuit elements: a capacitor, an inductor, a thermistor, and a linear negative resistor. The proposed system was analyzed with MATLAB R2018 through some numerical methods, such as largest Lyapunov exponent spectrum (LLE), phase diagram, Poincaré map, dynamic map, and time-domain waveform. The results revealed 11 kinds of chaotic attractors, 4 kinds of periodic attractors, and some attractive characteristics (such as coexistence attractors and transient transition behaviors). In addition, spectral entropy and sample entropy are adopted to analyze the phenomenon of coexisting attractors. The theoretical analysis and numerical simulation demonstrate that the system has rich dynamic characteristics.

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Heterogeneous and Homogenous Multistabilities in a Novel 4D Memristor-Based Chaotic System with Discrete Bifurcation Diagrams

Complexity ◽

10.1155/2020/2408460 ◽

2020 ◽

Vol 2020 ◽

pp. 1-15

Author(s):

Lilian Huang ◽

Wenju Yao ◽

Jianhong Xiang ◽

Zefeng Zhang

Keyword(s):

Chaotic System ◽

Chaotic Systems ◽

Large Range ◽

Circuit Simulation ◽

Chaotic Attractors ◽

Bifurcation Diagrams ◽

Coexisting Attractors ◽

Initial Values ◽

The Relationship ◽

New System

In this paper, a new 4D memristor-based chaotic system is constructed by using a smooth flux-controlled memristor to replace a resistor in the realization circuit of a 3D chaotic system. Compared with general chaotic systems, the chaotic system can generate coexisting infinitely many attractors. The proposed chaotic system not only possesses heterogeneous multistability but also possesses homogenous multistability. When the parameters of system are fixed, the chaotic system only generates two kinds of chaotic attractors with different positions in a very large range of initial values. Different from other chaotic systems with continuous bifurcation diagrams, this system has discrete bifurcation diagrams when the initial values change. In addition, this paper reveals the relationship between the symmetry of coexisting attractors and the symmetry of initial values in the system. The dynamic behaviors of the new system are analyzed by equilibrium point and stability, bifurcation diagrams, Lyapunov exponents, and phase orbit diagrams. Finally, the chaotic attractors are captured through circuit simulation, which verifies numerical simulation.

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