scholarly journals Coexisting Multiple Attractors in a Fourth Order Chua’s Circuit with Experimental Verifications by Analog and Digital Circuits

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Lei Zhu ◽  
Minghai Pan
Keyword(s):  
Fourth Order ◽  
Digital Circuits ◽  
Chua’S Circuit ◽  
Multiple Attractors ◽  
Chua's Circuit ◽  
Analog And Digital Circuits

A New Fourth-Order Memristive Chaotic System and Its Generation

2015 ◽  
Vol 25 (11) ◽  
pp. 1550151 ◽  
Author(s):  
Yuxia Li ◽  
Xia Huang ◽  
Yiwen Song ◽  
Jinuan Lin
Keyword(s):  
Phase Diagram ◽  
Lyapunov Exponent ◽  
Chaotic System ◽  
Fourth Order ◽  
Bifurcation Analysis ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Diagram Analysis

In this paper, a new fourth-order memristive chaotic system is constructed on the basis of Chua's circuit. Chaotic behaviors are verified through a series of dynamical analyses, including Lyapunov exponent analysis, bifurcation analysis, and phase diagram analysis. In addition, chaos attractors in the newly-proposed system are implemented by hardware circuits.

HYPERCHAOS IN A CHUA'S CIRCUIT WITH TWO NEW ADDED BRANCHES

2008 ◽  
Vol 18 (04) ◽  
pp. 1151-1159 ◽  
Author(s):  
RUY BARBOZA
Keyword(s):  
Theoretical Analysis ◽  
Fourth Order ◽  
Current Source ◽  
Experimental Results ◽  
The Other ◽  
Chua’S Circuit ◽  
Series Connection ◽  
Chua's Circuit ◽  
Original Topology ◽  
Wide Range

In this work a fourth-order Chua's circuit, capable of generating hyperchaotic oscillations in a wide range of parameters, is presented. The circuit is obtained by adding two new branches to the original topology of the Chua's double scroll circuit. One of the added branches is a linear inductor-resistor series connection, and the other one is a nonlinear voltage-controlled current source. A theoretical analysis of the circuit equations is presented, along with numerical and experimental results.

Coexistence of Multiple Attractors in an Active Diode Pair Based Chua’s Circuit

2018 ◽  
Vol 28 (02) ◽  
pp. 1850019 ◽  
Author(s):  
Bocheng Bao ◽  
Huagan Wu ◽  
Li Xu ◽  
Mo Chen ◽  
Wen Hu
Keyword(s):  
Equilibrium Points ◽  
Chaotic Attractors ◽  
Chua’S Circuit ◽  
Multiple Attractors ◽  
Stable Point ◽  
Chua's Circuit ◽  
Coexistence Of Multiple Attractors ◽  
Dynamical Properties ◽  
Nonzero Equilibrium ◽  
Made In

This paper focuses on the coexistence of multiple attractors in an active diode pair based Chua’s circuit with smooth nonlinearity. With dimensionless equations, dynamical properties, including boundness of system orbits and stability distributions of two nonzero equilibrium points, are investigated, and complex coexisting behaviors of multiple kinds of disconnected attractors of stable point attractors, limit cycles and chaotic attractors are numerically revealed. The results show that unlike the classical Chua’s circuit, the proposed circuit has two stable nonzero node-foci for the specified circuit parameters, thereby resulting in the emergence of multistability phenomenon. Based on two general impedance converters, the active diode pair based Chua’s circuit with an adjustable inductor and an adjustable capacitor is made in hardware, from which coexisting multiple attractors are conveniently captured.

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.

ATTRACTORS OF FOURTH-ORDER CHUA'S CIRCUIT AND CHAOS CONTROL

2007 ◽  
Vol 17 (08) ◽  
pp. 2705-2722 ◽  
Author(s):  
XIAN LIU ◽  
JINZHI WANG ◽  
LIN HUANG
Keyword(s):  
Fourth Order ◽  
Chaos Control ◽  
Piecewise Linear ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Chua’S Circuit ◽  
Cubic Nonlinearity ◽  
Stabilizing Controller ◽  
Chua's Circuit ◽  
Kyp Lemma

In this paper, in order to show some interesting phenomena of fourth-order Chua's circuit with a piecewise-linear nonlinearity and with a smooth cubic nonlinearity and compare dynamics between them, different kinds of attractors and corresponding Lyapunov exponent spectra of systems are presented, respectively. The frequency-domain condition for absolute stability of a class of nonlinear systems is transformed into linear matrix inequality (LMI) by using the celebrated Kalman–Yakubovich–Popov (KYP) lemma. A stabilizing controller based on LMI is designed so that chaos oscillations of fourth-order Chua's circuit with the piecewise-linear nonlinearity disappear and chaotic or hyperchaotic trajectories of the system are led to the origin. Simulation results are provided to demonstrate the effectiveness of the method.

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