Toward the Use of Chua's Circuit in Education, Art and Interdisciplinary Research: Some Implementation and Opportunities

Leonardo ◽  
2013 ◽  
Vol 46 (5) ◽  
pp. 456-463 ◽  
Author(s):  
Francesca Bertacchini ◽  
Eleonora Bilotta ◽  
Lorella Gabriele ◽  
Pietro Pantano ◽  
Assunta Tavernise
Keyword(s):  
Computer Simulation ◽  
Dynamic Systems ◽  
Interdisciplinary Research ◽  
Digital Images ◽  
Musical Instruments ◽  
Strange Attractors ◽  
Chua’S Circuit ◽  
Design Elements ◽  
Chua's Circuit ◽  
Virtual Museums

This paper considers the merging of Chaos with art, including such forms as digital images, sounds and music, based on dynamic systems derived from Chua's Circuit and using appropriate coding methods. Design elements, logos, musical instruments, software environments, multimedia theater performances and virtual museums with strange attractors have also been realized. In the field of education, the paper introduces environments that have foreseen the virtual manipulation of patterns derived from Chua's Circuit, which has fostered a deeper understanding of the evolution of dynamic systems through computer simulation.

STRANGE ATTRACTORS IN PERIODICALLY KICKED CHUA'S CIRCUIT

2005 ◽  
Vol 15 (01) ◽  
pp. 83-98 ◽  
Author(s):  
QIUDONG WANG ◽  
ALI OKSASOGLU
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Numerical Simulations ◽  
Autonomous System ◽  
Strange Attractors ◽  
External Forcing ◽  
Chua’S Circuit ◽  
New Developments ◽  
Chua's Circuit

In this paper, we discuss a new mechanism for chaos in light of some new developments in the theory of dynamical systems. It was shown in [Wang & Young, 2002b] that strange attractors occur when an autonomous system undergoing a generic Hopf bifurcation is subjected to a weak external forcing that is periodically turned on and off. For illustration purposes, we apply these results to the Chua's system. Derivation of conditions for chaos along with the results of numerical simulations are presented.

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.

DISCRETE RECONSTRUCTION OF STRANGE ATTRACTORS OF CHUA’S CIRCUIT

1994 ◽  
Vol 04 (04) ◽  
pp. 853-864 ◽  
Author(s):  
LUIS A. AGUIRRE ◽  
S.A. BILLINGS
Keyword(s):  
Nonlinear Models ◽  
Sampling Rate ◽  
Strange Attractors ◽  
Largest Lyapunov Exponent ◽  
Chua’S Circuit ◽  
Adequate Model ◽  
Chua's Circuit ◽  
Model Structures ◽  
Model Affect

This work is concerned with the identification of discrete nonlinear models from time series of strange attractors emerging in Chua’s circuit. The quality of the models is assessed by estimating the largest Lyapunov exponent, the correlation dimension and by comparing the geometry of the reconstructed dynamics to the original attractors. The major aim of the paper is to investigate how parameters such as the discretization period, sampling rate and the number of terms in an estimated model affect the dynamics and to determine if there is any relationship among such parameters. Conclusions in this direction are believed to be especially relevant in determining adequate model structures in identification applications. This is known to be critical in the identification of nonlinear systems.

FREQUENCY SWITCHED CHUA'S CIRCUIT: EXPERIMENTAL DYNAMICS CHARACTERIZATION

2001 ◽  
Vol 11 (01) ◽  
pp. 231-239 ◽  
Author(s):  
LUCIANO CANTELLI ◽  
LUIGI FORTUNA ◽  
MATTIA FRASCA ◽  
ALESSANDRO RIZZO
Keyword(s):  
Strange Attractors ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Experimental Dynamics ◽  
Switching Signal ◽  
Hysteresis Phenomena

In this letter the so-called frequency switched Chua's circuit is presented. Its realization is based on the introduction of a switch device into the Chua's circuit, realized by using three State-Controlled CNN cells. The dynamics of this system has been investigated both numerically and experimentally with respect to the frequency of the switch enabling signal. It exhibits different strange attractors, according to the variation of the frequency of the switching signal. Moreover, very strange frequency hysteresis phenomena demonstrating the peculiarity of the introduced circuit have been revealed.

STRANGE ATTRACTORS AND DYNAMICAL MODELS

1993 ◽  
Vol 03 (01) ◽  
pp. 1-10 ◽  
Author(s):  
L. P. SHIL'NIKOV
Keyword(s):  
Strange Attractors ◽  
Chua’S Circuit ◽  
Dynamical Models ◽  
Chua's Circuit

Three main types of strange attractors are described; namely hyperbolic, Lorenz-type and quasiattractors. In addition, a recent family of quasiattractors originating from Chua's circuit is briefly described. In connection with the strange attractors, we stress that models having quasiattractors containing structurally unstable homoclinic Poincaré orbits are "bad", in the sense of Ref. 24.

ON ENTROPY OF CHUA'S CIRCUITS

2005 ◽  
Vol 15 (05) ◽  
pp. 1823-1828 ◽  
Author(s):  
XIAO-SONG YANG ◽  
QINGDU LI
Keyword(s):  
Computer Simulation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Topological Entropy ◽  
Poincaré Map ◽  
Chua’S Circuit ◽  
Poincare Map ◽  
Chua's Circuit

In this paper we revisit the well-known Chua's circuit and give a discussion on entropy of this circuit. We present a formula for the topological entropy of a Chua's circuit in terms of the Poincaré map derived from the ordinary differential equations of this Chua's circuit by computer simulation arguments.

STRANGE ATTRACTORS OF THE SHIL'NIKOV TYPE IN CHUA'S CIRCUIT

1993 ◽  
Vol 03 (05) ◽  
pp. 1293-1298
Author(s):  
M. BLÁZQUEZ ◽  
E. TUMA
Keyword(s):  
Equilibrium Point ◽  
Homoclinic Orbit ◽  
Chaotic Behavior ◽  
Strange Attractors ◽  
Heteroclinic Orbits ◽  
Chua’S Circuit ◽  
Closed Contour ◽  
Chua's Circuit ◽  
Focus Type

The chaotic behavior of the solutions of Chua's circuit is studied in the neighborhood of a homoclinic orbit to an equilibrium point of the saddle-focus type and in a neighborhood of two heteroclinic orbits to saddle-focus points which form a closed contour.

SYNCHRONIZATION OF CHAOS IN A MODIFIED CHUA’S CIRCUIT USING CONTINUOUS CONTROL

1996 ◽  
Vol 06 (11) ◽  
pp. 2101-2117 ◽  
Author(s):  
YUAN-ZHAO YIN
Keyword(s):  
Computer Simulation ◽  
Bifurcation Control ◽  
Continuous Control ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Parallel Circuit ◽  
Control And Synchronization

We modify Chua’s circuit by adding an RC parallel circuit into the L-arm in Chua’s circuit. The bifurcation, control and synchronization of the modified Chua’s circuit has been studied by computer simulation.

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