scholarly journals Analysis of stability and bifurcations of limit cycles in Chua's circuit through the harmonic-balance approach

1999 ◽  
Vol 46 (8) ◽  
pp. 881-890 ◽  
Author(s):  
F. Bonani ◽  
M. Gilli
Keyword(s):  
Limit Cycles ◽  
Harmonic Balance ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Balance Approach ◽  
Analysis Of Stability ◽  
Stability And Bifurcations

CONTROL OF CHUA'S CIRCUIT

1993 ◽  
Vol 03 (01) ◽  
pp. 173-194 ◽  
Author(s):  
TOM T. HARTLEY ◽  
FARAMARZ MOSSAYEBI
Keyword(s):  
Control Theory ◽  
State Space ◽  
Chaotic System ◽  
Harmonic Balance ◽  
Period Doubling ◽  
Chua’S Circuit ◽  
Input Output ◽  
Chua's Circuit ◽  
Control Approach ◽  
Balance Approach

This paper considers the control of a polynomial variant of the original Chua's circuit. Both state space techniques and input-output techniques are presented. It is shown that standard control theory approaches can easily accommodate a chaotic system. Furthermore, it is shown that a harmonic balance approach could predict the period doubling phenomenon and onset of the double scroll chaos, as well as providing a control approach.

A HARMONIC BALANCE APPROACH FOR CHAOS PREDICTION: CHUA’S CIRCUIT

1992 ◽  
Vol 02 (01) ◽  
pp. 61-79 ◽  
Author(s):  
R. GENESIO ◽  
A. TESI
Keyword(s):  
Harmonic Balance ◽  
Complex Dynamics ◽  
Heuristic Method ◽  
Prediction Algorithm ◽  
Chua’S Circuit ◽  
Describing Function ◽  
Chua's Circuit ◽  
Design Engineers ◽  
Balance Principle ◽  
Practical Engineering

The paper proposes a practical engineering approach for predicting chaotic dynamics in an important class of nonlinear systems. The aim of this approach is to provide a heuristic method of analysis which can give reasonably accurate answers but is far simpler to apply than other more rigorous methods based on nonlinear dynamics. Our approach is founded on the harmonic balance principle and uses standard describing function techniques well known to design engineers. Our method consists of a synergism of two independent techniques, each one constituting a possible mechanism for chaos. These two techniques are combined into a single algorithm which is highly efficient computationally, taking only a fraction of the time normally required by other more exact procedures. In order to present and illustrate our algorithm clearly, and in order to compare its predictions with readily available results obtained by rigorous methods, we have chosen Chua’s circuit as a vehicle to demonstrate the effectiveness of this approach. Chua’s circuit was chosen not only for the huge amount of results already published concerning the dynamics of this system, but also because it represents a real physical system easily built in the laboratory, and whose simple mathematical model has proven to be realistic and mathematically tractable. Although our algorithm does not guarantee its prediction is fully reliable, any more than the widely used describing function method does, its significance is based entirely on the empirical evidence that it yields qualitatively correct, though not exact, results for all of the chaotic phenomena that we have investigated in Chua’s circuit, as well as in many other chaotic systems. We hope therefore that our chaos prediction algorithm will find practical uses among engineers and scientists not familiar with more specialized mathematical approaches, in search of a simple and practical, although not rigorous, tool for analyzing systems with complex dynamics.

A BIPARAMETRIC BIFURCATION IN 3D CONTINUOUS PIECEWISE LINEAR SYSTEMS WITH TWO ZONES: APPLICATION TO CHUA'S CIRCUIT

2007 ◽  
Vol 17 (02) ◽  
pp. 445-457 ◽  
Author(s):  
E. FREIRE ◽  
E. PONCE ◽  
J. ROS
Keyword(s):  
Hopf Bifurcation ◽  
Linear Systems ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Piecewise Linear ◽  
Continuous Systems ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Piecewise Linear Systems ◽  
Limit Cycle Bifurcation

In this paper, a possible degeneration of the focus-center-limit cycle bifurcation for piecewise smooth continuous systems is analyzed. The case of continuous piecewise linear systems with two zones is considered, and the coexistence of two limit cycles for certain values of parameters is justified. Finally, the Chua's circuit is shown to exhibit the analyzed bifurcation. The obtained bifurcation set in the parameter plane is similar to the degenerate Hopf bifurcation for differentiable systems.

FREQUENCY DOMAIN METHOD FOR THE DICHOTOMY OF MODIFIED CHUA'S EQUATIONS

2005 ◽  
Vol 15 (08) ◽  
pp. 2485-2505 ◽  
Author(s):  
ZHISHENG DUAN ◽  
JIN-ZHI WANG ◽  
LIN HUANG
Keyword(s):  
Computer Simulation ◽  
Limit Cycles ◽  
Chaotic Attractors ◽  
Output Coupling ◽  
Frequency Domain Method ◽  
Chua’S Circuit ◽  
Single Variable ◽  
Nonlinear Functions ◽  
Chua's Circuit ◽  
Input And Output

On condition of dichotomy, it is pointed out that in Lorenz and a kind of Rössler-like system chaotic attractors or limit cycles will disappear if nonlinearity of the product of two variables is replaced by some single variable nonlinearity, for example, nonlinearity of Chua's circuit. Furthermore, an extended Chua's circuit with two nonlinear functions is presented. By computer simulation it is shown that oscillating phenomena in the extended Chua's circuit are richer than the single Chua's circuit. The corresponding extension for smooth Chua's equations is also considered. The effects of input and output coupling are analyzed for the extended Chua's circuit.

scholarly journals HARMONIC BALANCE ANALYSIS OF THE GENERALIZED CHUA'S CIRCUIT

2006 ◽  
Vol 16 (08) ◽  
pp. 2325-2332 ◽  
Author(s):  
F. ACAR SAVACI ◽  
SERKAN GÜNEL
Keyword(s):  
Harmonic Balance ◽  
Piecewise Linear ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Describing Functions ◽  
Balance Principle ◽  
Harmonic Balance Analysis ◽  
Balance Analysis

In this paper, the harmonic balance analysis of Generalized Chua's circuit exhibiting n-scroll attractors has been accomplished. The dual-input describing functions of the piecewise-linear characteristics of Chua's diode have been obtained and based on the harmonic balance principle, the existence and the locations of the n-scrolls have been verified.

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