CONTROLLING CHAOS IN CHUA'S CIRCUIT

1993 ◽  
Vol 03 (01) ◽  
pp. 109-117 ◽  
Author(s):  
G. A. JOHNSON ◽  
T. E. TIGNER ◽  
E. R. HUNT
Keyword(s):  
Periodic Orbits ◽  
Chaotic Behavior ◽  
Autonomous Systems ◽  
Control Technique ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Periodically Driven ◽  
Single Orbit ◽  
Occasional Proportional Feedback ◽  
Control Circuits

The occasional proportional feedback (OPF) control technique has been successful in stabilizing periodic orbits in both periodically driven and autonomous systems undergoing chaotic behavior. By applying this technique to the well-known Chua's circuit, we are able to control a variety of periodic orbits including single-correction, low-period orbits and multiple-correction, high-period orbits. Also, by employing two control circuits, we are able to stabilize orbits that visit both regions of Chua's circuit's double-scroll attractor, applying corrections in each of these regions during a single orbit.

CONTROLLING CHAOS IN A SIMPLE AUTONOMOUS SYSTEM: CHUA’S CIRCUIT

1993 ◽  
Vol 03 (03) ◽  
pp. 789-792 ◽  
Author(s):  
G.A. JOHNSON ◽  
E.R. HUNT
Keyword(s):  
Periodic Orbits ◽  
Chaotic Behavior ◽  
Autonomous Systems ◽  
Control Technique ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Periodically Driven ◽  
Single Orbit ◽  
Occasional Proportional Feedback ◽  
Control Circuits

The occasional proportional feedback (OPF) control technique has been successful in stabilizing periodic orbits in both periodically driven and autonomous systems undergoing chaotic behavior. By applying this technique to the well-known Chua’s circuit, we are able to control a variety of periodic orbits including single-correction, low-period orbits and multiple-correction, high-period orbits. Also, by employing two control circuits, we are able to stabilize orbits that visit both regions of Chua’s circuit’s double-scroll attractor, applying corrections in each of these regions during a single orbit.

EXPERIMENTAL VERIFICATION OF PYRAGAS’S CHAOS CONTROL METHOD APPLIED TO CHUA’S CIRCUIT

1994 ◽  
Vol 04 (06) ◽  
pp. 1703-1706 ◽  
Author(s):  
P. CELKA
Keyword(s):  
Periodic Orbits ◽  
Experimental Verification ◽  
Chaos Control ◽  
Control Method ◽  
Experimental Results ◽  
Experimental Setup ◽  
Chua’S Circuit ◽  
Unstable Periodic Orbits ◽  
Chua's Circuit

We have built an experimental setup to apply Pyragas’s [1992, 1993] control method in order to stabilize unstable periodic orbits (UPO) in Chua’s circuit. We have been able to control low period UPO embedded in the double scroll attractor. However, experimental results show that the control method is useful under some restrictions we will discuss.

CONTROL OF n-SCROLL CHUA'S CIRCUIT

2009 ◽  
Vol 19 (11) ◽  
pp. 3813-3822 ◽  
Author(s):  
ABDELKRIM BOUKABOU ◽  
BILEL SAYOUD ◽  
HAMZA BOUMAIZA ◽  
NOURA MANSOURI
Keyword(s):  
Numerical Simulations ◽  
Fixed Points ◽  
Periodic Orbits ◽  
Predictive Control ◽  
Control Method ◽  
Sufficient Conditions ◽  
Chua’S Circuit ◽  
Unstable Periodic Orbits ◽  
Chua's Circuit ◽  
Necessary And Sufficient

This paper addresses the control of unstable fixed points and unstable periodic orbits of the n-scroll Chua's circuit. In a first step, we give necessary and sufficient conditions for exponential stabilization of unstable fixed points by the proposed predictive control method. In addition, we show how a chaotic system with multiple unstable periodic orbits can be stabilized by taking the system dynamics from one UPO to another. Control performances of these approaches are demonstrated by numerical simulations.

EXPERIMENTAL STUDY OF CFOA-BASED INDUCTORLESS CHUA'S CIRCUIT

2004 ◽  
Vol 14 (04) ◽  
pp. 1369-1374 ◽  
Author(s):  
RECAI KILIÇ
Keyword(s):  
Experimental Study ◽  
High Frequency ◽  
Chaotic Behavior ◽  
Comparative Investigation ◽  
Experimental Setup ◽  
Chua’S Circuit ◽  
Current Feedback ◽  
Chua's Circuit ◽  
Op Amps ◽  
High Frequency Performance

The current feedback op amps (CFOAs), with some significant advantages over the conventional op amps, have been used instead of voltage op amps (VOAs) in new implementations of Chua's circuit. In our previous study, after providing a comparative investigation of CFOA-based realizations of Chua's circuit in the literature, we have also presented an alternative inductorless CFOA-based realization of Chua's circuit, and the circuit's chaotic behavior by Pspice simulations. In this paper, we investigate CFOA-based Chua's circuit by constructing an experimental setup, and testing the performance of the proposed implementation at different frequencies. Its excellent high frequency performance was experimentally verified.

CHAOTIC BEHAVIOR OF ORBITS CLOSE TO A HETEROCLINIC CONTOUR

1996 ◽  
Vol 06 (01) ◽  
pp. 69-79 ◽  
Author(s):  
M. BLÁZQUEZ ◽  
E. TUMA
Keyword(s):  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Chua’S Circuit ◽  
Closed Contour ◽  
Chua's Circuit ◽  
Infinite Dimensional ◽  
Focus Type

We study the behavior of the solutions in a neighborhood of a closed contour formed by two heteroclinic connections to two equilibrium points of saddle-focus type. We consider both the three-dimensional case, as in the well-known Chua's circuit, as well as the infinite-dimensional case.

KNOTTED PERIODIC ORBITS IN CHUA’S CIRCUIT

1994 ◽  
Vol 04 (03) ◽  
pp. 609-621
Author(s):  
Lj. KOCAREV ◽  
Z. TASEV ◽  
D. DIMOVSKI ◽  
L.O. CHUA
Keyword(s):  
Periodic Orbits ◽  
Chaotic Attractors ◽  
Chua’S Circuit ◽  
Topological Properties ◽  
Chua's Circuit ◽  
Spiral Type ◽  
Lower Period

Induced templates for two members of Chua’s attractors: spiral-type and double-scroll chaotic attractors are computed using the orbits of lower period. The template describes the topological properties of periodic orbits embedded in the attractor. It is identified by a set of integers which characterize the attractor. The templates are confirmed by investigating orbits of higher period.

CHARACTERISATION OF CHAOS IN CHUA'S OSCILLATOR IN TERMS OF UNSTABLE PERIODIC ORBITS

1993 ◽  
Vol 03 (02) ◽  
pp. 411-429 ◽  
Author(s):  
MACIEJ J. OGORZAŁEK ◽  
ZBIGNIEW GALIAS
Keyword(s):  
Periodic Orbits ◽  
Picture Book ◽  
Chaotic Attractors ◽  
Chua’S Circuit ◽  
Unstable Periodic Orbits ◽  
Chua's Circuit ◽  
Chua’S Oscillator ◽  
Canonical Chua’S Circuit

We present a picture book of unstable periodic orbits embedded in typical chaotic attractors found in the canonical Chua's circuit. These include spiral Chua's, double-scroll Chua's and double hook attractors. The "skeleton" of unstable periodic orbits is specific for the considered attractor and provides an invariant characterisation of its geometry.

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