scholarly journals Hidden Multistability in a Memristor-Based Cellular Neural Network

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Birong Xu ◽  
Hairong Lin ◽  
Guangyi Wang
Keyword(s):  
Neural Network ◽  
Simulation Analysis ◽  
Equilibrium Points ◽  
Cellular Neural Network ◽  
Nonlinear Phenomena ◽  
Hidden Attractors ◽  
Coexisting Attractors ◽  
Dynamical Behaviors ◽  
Circuit Simulations

In this paper, we report a novel memristor-based cellular neural network (CNN) without equilibrium points. Dynamical behaviors of the memristor-based CNN are investigated by simulation analysis. The results indicate that the system owns complicated nonlinear phenomena, such as hidden attractors, coexisting attractors, and initial boosting behaviors of position and amplitude. Furthermore, both heterogeneous multistability and homogenous multistability are found in the CNN. Finally, Multisim circuit simulations are performed to prove the chaotic characteristics and multistability of the system.

scholarly journals A locally Active Discrete Memristor Model and Its Application in a Hyperchaotic Map

2021 ◽  
Author(s):  
Minglin Ma ◽  
Yang Yang ◽  
Zhicheng Qiu ◽  
Yuexi Peng ◽  
Yichuang Sun ◽  
...  
Keyword(s):  
Simulation Analysis ◽  
Engineering Application ◽  
Two Dimensional ◽  
Coexisting Attractors ◽  
Distribution Diagram ◽  
Dynamical Behaviors ◽  
Memristive System ◽  
Definition Of ◽  
First Time ◽  
Lyapunov Exponent Spectrum

Abstract The continuous memristor is a popular topic of research in recent years, however, there is rare discussion about the discrete memristor model, especially the locally active discrete memristor model. This paper proposes a locally active discrete memristor model for the first time and proves the three fingerprints characteristics of this model according to the definition of generalized memristor. A novel hyperchaotic map is constructed by coupling the discrete memristor with a two-dimensional generalized square map. The dynamical behaviors are analyzed with attractor phase diagram, bifurcation diagram, Lyapunov exponent spectrum, and dynamic behavior distribution diagram. Numerical simulation analysis shows that there is significant improvement in the hyperchaotic area, the quasi-periodic area and the chaotic complexity of the two-dimensional map when applying the locally active discrete memristor. In addition, antimonotonicity and transient chaos behaviors of system are reported. In particular, the coexisting attractors can be observed in this discrete memristive system, resulting from the different initial values of the memristor. Results of theoretical analysis are well verified with hardware experimental measurements. This paper lays a great foundation for future analysis and engineering application of the discrete memristor and relevant the study of other hyperchaotic maps.

Dynamical analysis, FPGA implementation and synchronization for secure communication of new chaotic system with hidden and coexisting attractors

2021 ◽  
Author(s):  
Qiang Lai ◽  
Ziling Wang ◽  
Paul Didier Kamdem Kuate
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Analog Circuit ◽  
Control Method ◽  
Simulation Analysis ◽  
Period Doubling ◽  
Fpga Implementation ◽  
Dynamical Analysis ◽  
Hidden Attractors ◽  
Coexisting Attractors

This paper proposes an interesting autonomous chaotic system with hidden attractors and coexisting attractors. The system has no equilibrium, one equilibrium, three equilibria and line equilibria for different parameter regions. The existence of hidden attractors and coexisting attractors of the system has been revealed by using simulation analysis. The bifurcation diagram shows the period-doubling bifurcation route to chaos with the variation of parameters. The analog circuit and FPGA implementation of the system are presented. The synchronization for secure communication of the system is investigated. The synchronization conditions are established by using the adaptive control method.

scholarly journals Analyzing stability of equilibrium points in impulsive neural network models involving generalized piecewise alternately advanced and retarded argument

2021 ◽  
Author(s):  
Kuo-Shou Chiu
Keyword(s):  
Neural Network ◽  
Global Exponential Stability ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Network Models ◽  
Cellular Neural Network ◽  
Retarded Argument ◽  
Impulsive Systems ◽  
Neural Network Models ◽  
Banach’S Fixed Point Theorem

In this paper, we investigate the models of the impulsive cellular neural network with piecewise alternately advanced and retarded argument of generalized argument (in short IDEPCAG). To ensure the existence, uniqueness and global exponential stability of the equilibrium state, several new sufficient conditions are obtained, which extend the results of the previous literature. The method is based on utilizing Banach’s fixed point theorem and a new IDEPCAG’s Gronwall inequality. The criteria given are easy to check and when the impulsive effects do not affect, the results can be extracted from those of the non-impulsive systems. Typical numerical simulation examples are used to show the validity and effectiveness of proposed results. We end the article with a brief conclusion.

A Chaotic System with Different Families of Hidden Attractors

2016 ◽  
Vol 26 (08) ◽  
pp. 1650139 ◽  
Author(s):  
Viet-Thanh Pham ◽  
Christos Volos ◽  
Sajad Jafari ◽  
Sundarapandian Vaidyanathan ◽  
Tomasz Kapitaniak ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Chaotic System ◽  
Infinite Number ◽  
Mathematical Analysis ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
Circuit Implementation ◽  
Hidden Attractors ◽  
Dynamical Behaviors

The presence of hidden attractors in dynamical systems has received considerable attention recently both in theory and applications. A novel three-dimensional autonomous chaotic system with hidden attractors is introduced in this paper. It is exciting that this chaotic system can exhibit two different families of hidden attractors: hidden attractors with an infinite number of equilibrium points and hidden attractors without equilibrium. Dynamical behaviors of such system are discovered through mathematical analysis, numerical simulations and circuit implementation.

scholarly journals A New 4D Chaotic System with Two-Wing, Four-Wing, and Coexisting Attractors and Its Circuit Simulation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Lilian Huang ◽  
Zefeng Zhang ◽  
Jianhong Xiang ◽  
Shiming Wang
Keyword(s):  
Numerical Simulation ◽  
Chaotic System ◽  
Dynamic Characteristics ◽  
Simulation Analysis ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Coexisting Attractors ◽  
System A ◽  
Simulation Results ◽  
New System

In order to further improve the complexity of chaotic system, a new four-dimensional chaotic system is constructed based on Sprott B chaotic system. By analyzing the system’s phase diagrams, symmetry, equilibrium points, and Lyapunov exponents, it is found that the system can generate not only both two-wing and four-wing attractors but also the attractors with symmetrical coexistence, and the dynamic characteristics of the new system constructed are more abundant. In addition, the system is simulated by Multisim software, and the simulation results show that the results of circuit simulation and numerical simulation analysis are basically the same.

Dynamical Analysis of Coupled Bidirectional FitzHugh–Nagumo Neuronal Networks With Multiple Delays

2019 ◽  
Vol 14 (6) ◽  
Author(s):  
Xiaochen Mao ◽  
Xiangyu Zhou ◽  
Tiantian Shi ◽  
Lei Qiao
Keyword(s):  
Neuronal Networks ◽  
Electronic Circuit ◽  
Dynamical Analysis ◽  
Chaotic Attractors ◽  
Multiple Delays ◽  
Coexisting Attractors ◽  
Science And Engineering ◽  
Chaotic Motions ◽  
Dynamical Behaviors ◽  
Circuit Simulations

Coupled neuronal networks have received considerable attention due to their important and extensive applications in science and engineering. This paper focuses on the nonlinear dynamics of delay-coupled bidirectional FitzHugh–Nagumo (FHN) neuronal networks through theoretical analysis, numerical computations, and circuit simulations. A variety of interesting dynamical behaviors of the network are explored, such as the coexistence of nontrivial equilibria and periodic solutions, different patterns of coexisting attractors, and even chaotic motions. An electronic circuit is designed and performed to validate the facticity of the complicated behaviors, such as multistability and chaotic attractors. It is shown that the circuit simulations reach an agreement with the obtained results.

Self-Excited and Hidden Attractors Found Simultaneously in a Modified Chua's Circuit

2015 ◽  
Vol 25 (05) ◽  
pp. 1550075 ◽  
Author(s):  
Bocheng Bao ◽  
Fengwei Hu ◽  
Mo Chen ◽  
Quan Xu ◽  
Yajuan Yu
Keyword(s):  
Saddle Point ◽  
Fourth Order ◽  
Nonlinear Phenomena ◽  
Chua’S Circuit ◽  
Hidden Attractors ◽  
Parameter Region ◽  
Chua's Circuit ◽  
First Order ◽  
Dynamical Behaviors

By replacing the Chua's diode in Chua's circuit with a first-order hybrid diode circuit, a fourth-order modified Chua's circuit is presented. The circuit has an unstable zero saddle point and two nonzero saddle-foci. By Routh–Hurwitz criterion, it is found that in a narrow parameter region, the two nonzero saddle-foci have a transition from unstable to stable saddle-foci, leading to generations of self-excited and hidden attractors in the modified Chua's circuit simultaneously, which have not been previously reported. Complex dynamical behaviors are investigated both numerically and experimentally. The results indicate that the proposed circuit exhibits complicated nonlinear phenomena including self-excited attractors, coexisting self-excited attractors, hidden attractors, and coexisting hidden attractors.

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