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. 

CHUA’S CIRCUIT: AN OVERVIEW TEN YEARS LATER

1994 ◽  
Vol 04 (02) ◽  
pp. 117-159 ◽  
Author(s):  
LEON O. CHUA
Keyword(s):  
Secure Communication ◽  
Vector Fields ◽  
Piecewise Linear ◽  
International Workshop ◽  
Noise Spectrum ◽  
Chaotic Regime ◽  
Practical Significance ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
New Phenomena

More than 200 papers, two special issues (Journal of Circuits, Systems, and Computers, March, June, 1993, and IEEE Trans. on Circuits and Systems, vol. 40, no. 10, October, 1993), an International Workshop on Chua’s Circuit: chaotic phenomena and applica tions at NOLTA’93, and a book (edited by R.N. Madan, World Scientific, 1993) on Chua’s circuit have been published since its inception a decade ago. This review paper attempts to present an overview of these timely publications, almost all within the last six months, and to identify four milestones of this very active research area. An important milestone is the recent fabrication of a monolithic Chua’s circuit. The robustness of this IC chip demonstrates that an array of Chua’s circuits can also be fabricated into a monolithic chip, thereby opening the floodgate to many unconventional applications in information technology, synergetics, and even music. The second milestone is the recent global unfolding of Chua’s circuit, obtained by adding a linear resistor in series with the inductor to obtain a canonical Chua’s circuit— now generally referred to as Chua’s oscillator. This circuit is most significant because it is structurally the simplest (it contains only 6 circuit elements) but dynamically the most complex among all nonlinear circuits and systems described by a 21-parameter family of continuous odd-symmetric piecewise-linear vector fields. The third milestone is the recent discovery of several important new phenomena in Chua’s circuits, e.g., stochastic resonance, chaos-chaos type intermittency, 1/f noise spectrum, etc. These new phenomena could have far-reaching theoretical and practical significance. The fourth milestone is the theoretical and experimental demonstration that Chua’s circuit can be easily controlled from a chaotic regime to a prescribed periodic or constant orbit, or it can be synchronized with 2 or more identical Chua’s circuits, operating in an oscillatory, or a chaotic regime. These recent breakthroughs have ushered in a new era where chaos is deliberately created and exploited for unconventional applications, e.g. secure communication.

Experimental study of stochastic resonance in a Chua’s circuit operating in a chaotic regime

2006 ◽  
Vol 219 (1) ◽  
pp. 93-100 ◽  
Author(s):  
Wojciech Korneta ◽  
Iacyel Gomes ◽  
Claudio R. Mirasso ◽  
Raúl Toral
Keyword(s):  
Experimental Study ◽  
Stochastic Resonance ◽  
Chaotic Regime ◽  
Chua’S Circuit ◽  
Chua's Circuit

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.

FRACTIONAL-ORDER CHUA'S CIRCUIT: TIME-DOMAIN ANALYSIS, BIFURCATION, CHAOTIC BEHAVIOR AND TEST FOR CHAOS

2008 ◽  
Vol 18 (03) ◽  
pp. 615-639 ◽  
Author(s):  
DONATO CAFAGNA ◽  
GIUSEPPE GRASSI
Keyword(s):  
Fractional Order ◽  
Time Domain ◽  
Decomposition Method ◽  
Chaotic Behavior ◽  
Adomian Decomposition Method ◽  
Time Domain Analysis ◽  
Point Of View ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Adomian Decomposition

In this tutorial the chaotic behavior of the fractional-order Chua's circuit is investigated from the time-domain point of view. The objective is achieved using the Adomian decomposition method, which enables the solution of the fractional differential equations to be found in closed form. By exploiting the capabilities offered by the decomposition method, the paper presents two remarkable findings. The first result is that a novel bifurcation parameter is identified, that is, the fractional-order q of the derivative. The second result is that chaos exists in the fractional Chua's circuit with order q = 1.05, which is the lowest order reported in literature for such circuits. Finally, a reliable and efficient binary test for chaos (called "0–1 test") is utilized to detect the presence of chaotic attractors in the system dynamics.

CHAOTIC BEATS IN A MODIFIED CHUA'S CIRCUIT: DYNAMIC BEHAVIOR AND CIRCUIT DESIGN

2004 ◽  
Vol 14 (09) ◽  
pp. 3045-3064 ◽  
Author(s):  
DONATO CAFAGNA ◽  
GIUSEPPE GRASSI
Keyword(s):  
State Space ◽  
Dynamic Behavior ◽  
Circuit Design ◽  
Time Domain ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Chaotic Beats ◽  
Chaotic Nature

This paper illustrates the recent phenomenon of chaotic beats in a modified version of Chua's circuit, driven by two sinusoidal inputs with slightly different frequencies. In order to satisfy the constraints imposed by the beats dynamics, a novel implementation of the voltage-controlled characteristic of the Chua diode is proposed. By using Pspice simulator, the behavior of the designed circuit is analyzed both in time-domain and state-space, confirming the chaotic nature of the phenomenon and the effectiveness of the approach.

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.

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