THE ANALYSIS OF THE STOCHASTICALLY FORCED PERIODIC ATTRACTORS FOR CHUA'S CIRCUIT

2004 ◽  
Vol 14 (11) ◽  
pp. 3981-3987 ◽  
Author(s):  
MIKHAIL YU. RYAGIN ◽  
LEV B. RYASHKO
Keyword(s):  
Sensitivity Analysis ◽  
Limit Cycle ◽  
Period Doubling ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Transition To Chaos ◽  
Stochastic Sensitivity ◽  
Periodic Attractors ◽  
The Matrix ◽  
Small Disturbances

This report shows the results of sensitivity analysis for Chua's circuit periodic attractors under small disturbances. Sensitivity analysis is based on the quasipotential method. Quasipotential's first approximation in the neighborhood of the limit cycle is defined by the matrix of orbital quadratic form, named stochastic sensitivity function (SSF). SSF is defined for the points of the nonperturbed limit cycle and can be computed using the numerical algorithm. Stochastic sensitivity of the limit cycles for the Chua's circuit period doubling cascade is investigated. The growth of the stochastic sensitivity under transition to chaos is shown.

MULTI-PARAMETER CRITICALITY IN CHUA'S CIRCUIT AT PERIOD-DOUBLING TRANSITION TO CHAOS

1996 ◽  
Vol 06 (01) ◽  
pp. 119-148 ◽  
Author(s):  
A. P. KUZNETSOV ◽  
S. P. KUZNETSOV ◽  
I. R. SATAEV ◽  
L. O. CHUA
Keyword(s):  
Period Doubling ◽  
Coupled Systems ◽  
Strict Sense ◽  
Chua’S Circuit ◽  
Dynamical Equations ◽  
Scaling Properties ◽  
Unidirectional Coupling ◽  
Chua's Circuit ◽  
Transition To Chaos ◽  
Two Systems

Investigation of non-Feigenbaum types of period-doubling universality is undertaken for a single Chua's circuit and for two systems with a unidirectional coupling. Some codimension-2 critical situations are found numerically that were known earlier for bimodal 1D maps. However, the simplest of them (tricritical) does not survive in a strict sense when the exact dynamical equations are used instead of the 1D map approximation. In coupled systems double Feigenbaum's point and bicritical behavior are found and studied. Scaling properties that are the same as in two logistic maps with a unidirectional coupling are illustrated.

The analysis of chaotic regimes in Chua’s circuit with smooth nonlinearity based on the matrix decomposition method

2019 ◽  
Vol 63 (4) ◽  
pp. 501-512
Author(s):  
A. M. Krot ◽  
U. A. Sychou
Keyword(s):  
Simulation Model ◽  
State Space ◽  
Decomposition Method ◽  
Matrix Decomposition ◽  
Chaotic Regime ◽  
Chua’S Circuit ◽  
Electric Circuits ◽  
Chua's Circuit ◽  
The Matrix ◽  
Matrix Series

The scope of this work are electric circuits or electronic devices with chaotic regimes, in particular the Chua’s circuit. A nonlinear analysis of chaotic attractors based on the Krot’s method of matrix decomposition of vector functions in state-space of complex systems has been used to investigate the Chua’s circuit with smooth nonlinearity. It includes an analysis of linear term of the matrix series as well as an estimation of influence of high order terms of this series on stability of complex system under investigation. Here the method of matrix decomposition has been applied to analysis of the Chua’s attractor. The terms of matrix series have been used to create a simulation model and to reconstruct an attractor of chaotic modes. The proposed simulation model makes it possible to separate an influence of nonlinearities on forming a chaotic regime of the Chua’s circuit. Usage of both the matrix decomposition method and computational experiment has allowed us to find out that the initial turbulence model proposed by L. D. Landau is suitable for set-up description of the chaotic regime of the Chua’s circuit. It is shown that a mode of hard self-excitation in the Chua’s circuit leads to its chaotic regime operating with a double-scroll attractor in the state-space. The results might be used to generate of chaotic oscillations or data encryption. 

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.

ARNOL’D TONGUES, DEVIL’S STAIRCASE, AND SELF-SIMILARITY IN THE DRIVEN CHUA’S CIRCUIT

1994 ◽  
Vol 04 (06) ◽  
pp. 1743-1753 ◽  
Author(s):  
LADISLAV PIVKA ◽  
ALEXANDER L. ZHELEZNYAK ◽  
LEON O. CHUA
Keyword(s):  
Initial Conditions ◽  
Period Doubling ◽  
Chua’S Circuit ◽  
Self Similarity ◽  
Devil's Staircase ◽  
Algebraic Form ◽  
Chua's Circuit ◽  
Recurrent Relations ◽  
Devil’S Staircase ◽  
Self Similar

Empirical recurrent relations, governing the structure of the devil’s staircase in the driven Chua’s circuit are given, which reflect the self-similar structure in an algebraic form. In particular, it turns out that the same formulas hold for both winding and period numbers, but with different “initial conditions”. Some of the finer details such as period-doubling along with numerous coexistence phenomena within staircases of mode-locked states have been revealed by computing high-resolution bifurcation diagrams.

Higher-Order Spectral Analysis to Detect Power-Frequency Mechanisms in a Driven Chua's Circuit

1997 ◽  
Vol 07 (06) ◽  
pp. 1431-1440 ◽  
Author(s):  
Domine M. W. Leenaerts
Keyword(s):  
Period Doubling ◽  
Peak Frequency ◽  
Higher Order ◽  
Nonlinear Interactions ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Power Frequency ◽  
Higher Order Spectra ◽  
Doubling Sequence ◽  
Dominant Frequencies

Higher-order spectra have been used to investigate nonlinear interactions between frequency modes in a driven Chua's circuit. The spectra show that an energy transfer takes place to the dominant frequencies in the circuit, i.e. the input frequency, the primary peak frequency and the harmonics of both frequencies. Other frequencies couplings become less important. Obviously, powers are (nonlinearly) related at different frequencies. When the circuit undergoes a period doubling sequence to chaos, the gain is increasing.

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.

NEW ATTRACTORS AND NEW BEHAVIORS IN THE PHOTO-CONTROLLED CHUA'S CIRCUIT

2009 ◽  
Vol 19 (01) ◽  
pp. 329-338 ◽  
Author(s):  
FADHIL RAHMA ◽  
LUIGI FORTUNA ◽  
MATTIA FRASCA
Keyword(s):  
Light Source ◽  
Period Doubling ◽  
Experimental Results ◽  
Chaotic Attractors ◽  
Chua’S Circuit ◽  
Light Control ◽  
Low Frequencies ◽  
Chua's Circuit ◽  
Intermittent Behavior ◽  
Period Doubling Bifurcations

In this brief communication, we introduce a Chua's circuit based on a photoresistor nonlinear device and experimentally investigate the effects of controlling it by a light source. Light control affects the dynamics of the circuit in several ways, and the circuit can be controlled to exhibit periodicity, period-doubling bifurcations and chaotic attractors. The dynamics of the circuit that operates at frequencies up to kilohertz is strongly influenced by using periodic driving signals at low frequencies. In particular, experimental results have shown that an unstable intermittent behavior can be observed and that this can be stabilized by using feedback. Synchronization of two circuits has also been investigated.

EXPERIMENTAL OBSERVATION OF ANTIMONOTONICITY IN CHUA'S CIRCUIT

1993 ◽  
Vol 03 (04) ◽  
pp. 1051-1055 ◽  
Author(s):  
Lj. KOCAREV ◽  
K. S. HALLE ◽  
K. ECKERT ◽  
L. O. CHUA
Keyword(s):  
Experimental Observation ◽  
Period Doubling ◽  
Chua’S Circuit ◽  
Chua's Circuit

Two different bifurcation patterns are experimentally observed in Chua's circuit. They show that antimonotonicity — inevitable reversals of period-doubling sequences, is a typical phenomenon in Chua's circuit.

CONTROLLING CHAOS IN A CHUA'S CIRCUIT USING NOTCH FILTERS

2009 ◽  
Vol 18 (06) ◽  
pp. 1137-1153 ◽  
Author(s):  
ASHRAF A. ZAHER ◽  
ABDULNASSER ABU-REZQ
Keyword(s):  
Power Spectrum ◽  
Period Doubling ◽  
Original System ◽  
Point Of View ◽  
Practical Implementation ◽  
Secure Communications ◽  
Chua’S Circuit ◽  
Notch Filters ◽  
Chua's Circuit ◽  
Processing Point

This paper explores the use of notch filters for the purpose of damping out chaotic oscillations. The design of the filter and the way it is interfaced to the system are investigated from a signal-processing point of view. A Chua's circuit, that has typical applications in synchronization and secure communications, is used to exemplify the suggested methodology where both theoretical and experimental results are provided. The power spectrum of the original system is analyzed to selectively damp-out portions of the power spectrum, thus truncating period-doubling, the original cause of chaos. Both single and double notch filters are explored to examine their effect on the performance of the modified system. Steady state analysis as well as issues regarding practical implementation are addressed and advantages and limitations of the proposed method are highlighted.

Strange Nonchaotic Attractors of Chua's Circuit with Quasiperiodic Excitation

1997 ◽  
Vol 07 (01) ◽  
pp. 227-238 ◽  
Author(s):  
Zhiwen Zhu ◽  
Zhong Liu
Keyword(s):  
Lyapunov Exponents ◽  
Period Doubling ◽  
Period Doubling Bifurcation ◽  
Smooth Transition ◽  
Chua’S Circuit ◽  
Poincaré Maps ◽  
Strange Nonchaotic Attractor ◽  
Chua's Circuit ◽  
Poincare Maps ◽  
Strange Nonchaotic Attractors

This paper focuses attention on strange nonchaotic attractor of Chua's circuit with two-frequency quasiperiodic excitation. Existence of the attractor is confirmed by calculating several characterizing quantities such as Lyapunov exponents, Poincaré maps, double Poincaré maps and so on. Two basic mechanisms are described for the development of the strange nonchaotic attractor from two-frequency quasiperiodic state (torus solution). One of them is torus-doubling bifurcation followed by a smooth transition from the torus attractor to the strange nonchaotic attractor; and another is that the torus does not undergo period-doubling bifurcation at all; instead, the torus attractor gradually becomes wrinkled, and eventually becomes strange but nonchaotic.

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