Stability Analysis of Fourth-Order Chua’s Circuit

2011 ◽  
pp. 241-250
Author(s):  
Chunfang Miao ◽  
Yunquan Ke
Keyword(s):  
Stability Analysis ◽  
Fourth Order ◽  
Chua’S Circuit ◽  
Chua's Circuit

Memristive oscillator based on Chua’s circuit: stability analysis and hidden dynamics

2017 ◽  
Vol 88 (4) ◽  
pp. 2577-2587 ◽  
Author(s):  
Ronilson Rocha ◽  
Jothimurugan Ruthiramoorthy ◽  
Thamilmaran Kathamuthu
Keyword(s):  
Stability Analysis ◽  
Chua’S Circuit ◽  
Chua's Circuit

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.

Fixed Point Stability Analysis of Chua's Circuit: A Case Study with a Real Circuit

1997 ◽  
Vol 07 (02) ◽  
pp. 111-115 ◽  
Author(s):  
Luis A. Aguirre ◽  
Leonardo A. B. Tôrres
Keyword(s):  
Fixed Point ◽  
Stability Analysis ◽  
Internal Resistance ◽  
Short Paper ◽  
Chua’S Circuit ◽  
Chaotic Oscillations ◽  
Chua's Circuit

This short paper discusses the effect of the internal resistance of the inductor in Chua's circuit which is often neglected by many even when actual implementation is intended. Using a fixed point stability analysis it is shown that varying the inductor resistance it is possible to suppress or allow chaotic oscillations. The results reported in this paper have clear consequences for the control of Chua's circuit.

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.

Stability Analysis and Mapping of Multiple Dynamics of Chua’s Circuit in Full Four-Parameter Spaces

2015 ◽  
Vol 25 (13) ◽  
pp. 1530037 ◽  
Author(s):  
Ronilson Rocha ◽  
Rene Orlando Medrano-T.
Keyword(s):  
Stability Analysis ◽  
Theoretical Analysis ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Chua’S Circuit ◽  
Parameter Spaces ◽  
Chua's Circuit ◽  
Describing Functions ◽  
Route To Chaos ◽  
The Stability

The stability analysis is used in order to identify and to map different dynamics of Chua’s circuit in full four-parameter spaces. The study is performed using describing functions that allow to identify fixed point, periodic orbit, and unstable states with relative accuracy, as well as to predict route to chaos and hidden dynamics that conventional computational methods do not detect. Numerical investigations based on the computation of eigenvalues and Lyapunov exponents partially support the predictions obtained from the theoretical analysis since they do not capture the multiple dynamics that can coexist in the operation of Chua’s circuit. Attractors obtained from initial conditions outside of neighborhoods of the equilibrium points confirm the multiplicity of dynamics in the operation of Chua’s circuit and corroborate the theoretical analysis.

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