Suppression of chaos by incommensurate excitations: Theory and experimental confirmations

We consider the effects of parametric perturbation on the onset of chaos in different dynamical systems. Favoring or suppression of chaos was observed depending on the phase or the frequency of the periodic perturbation. A lowering of the threshold of chaos was observed in an electronic device simulating a Josephson-Junction model and the suppression of chaos was obtained in a bistable mechanical device. We showed that in case of spatial instability in a sample of liquid crystal, the action of the parametric perturbation is to modify the velocity and the onset of the defects. Considering that the emergence of defects precedes the threshold of spatio-temporal chaos, we infer that parametric perturbation can modify the threshold of chaos in this spatial dynamical system.

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Suppression of chaos in a class of non-linear systems by disturbance observers

Journal of Sound and Vibration ◽

10.1016/s0022-460x(03)00630-8 ◽

2004 ◽

Vol 271 (1-2) ◽

pp. 481-491 ◽

Cited By ~ 3

Author(s):

S.M. Shahruz ◽

L.R. Siva

Keyword(s):

Linear Systems ◽

Non Linear ◽

Non Linear Systems ◽

Suppression Of Chaos

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Suppression of chaos in 1-D maps

Physics Letters A ◽

10.1016/0375-9601(88)90607-x ◽

1988 ◽

Vol 130 (4-5) ◽

pp. 267-270 ◽

Cited By ~ 2

Author(s):

Aaron B. Corbet

Keyword(s):

Suppression Of Chaos

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CONTROLLING OF CHAOS IN BONHOEFFER- VAN DER POL OSCILLATOR

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127492000197 ◽

1992 ◽

Vol 02 (01) ◽

pp. 201-204 ◽

Cited By ~ 40

Author(s):

S. RAJASEKAR ◽

M. LAKSHMANAN

Keyword(s):

External Noise ◽

Chaotic Regime ◽

Van Der Pol Oscillator ◽

Control Algorithms ◽

External Parameter ◽

Parametric Perturbation ◽

Van Der Pol ◽

Controlling Of Chaos ◽

Adaptive Control Algorithm ◽

Suppression Of Chaos

In this letter controlling of chaos in Bonhoeffer-van der Pol oscillator is investigated using various different control algorithms. Specifically, using an adaptive control algorithm we analyse the resetting of the system dynamics from a chaotic attractor to a limit cycle attractor. We demonstrate that, starting from a chaotic regime, it is possible to bring the system to a regular regime by means of a small parametric perturbation as well as by the addition of a weak external force. It is then shown that one can eliminate chaotic evolution by stabilizing an unstable periodic orbit by making small adjustments to an external parameter. Finally, we show the suppression of chaos by adding appropriate external noise.

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CHAOS CONTROL IMPLEMENTATION BY INTERRUPTED ELECTRIC CIRCUIT WITH SWITCHING DELAY

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127409024128 ◽

2009 ◽

Vol 19 (07) ◽

pp. 2359-2362

Author(s):

TAKUJI KOUSAKA ◽

TETSUSHI UETA ◽

YUE MA

Keyword(s):

Periodic Orbit ◽

Chaos Control ◽

Electric Circuit ◽

Unstable Periodic Orbit ◽

Chaotic Circuit ◽

Return Map ◽

Switching Delay ◽

Suppression Of Chaos ◽

Control Implementation

We have demonstrated that the chaotic circuit with a switching delay is modeled by a return map, and a controller for the suppression of chaos is proposed. A circuit representing a controller stabilizing a period-1 unstable periodic orbit in an interrupted electric circuit with a certain switching delay is also discussed.

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Optimal Control of a Chaotic Map: Fixed Point Stabilization and Attractor Confinement

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127497000315 ◽

1997 ◽

Vol 07 (02) ◽

pp. 437-446 ◽

Cited By ~ 22

Author(s):

C. Piccardi ◽

L. L. Ghezzi

Keyword(s):

Optimal Control ◽

Fixed Point ◽

Optimal Control Problem ◽

Control Problem ◽

Chaotic Attractor ◽

Chaotic Map ◽

Optimal Controller ◽

Control Of Chaos ◽

One Dimensional ◽

Suppression Of Chaos

Optimal control is applied to a chaotic system. Reference is made to a well-known one-dimensional map. Firstly, attention is devoted to the stabilization of a fixed point. An optimal controller is obtained and compared with other controllers which are popular in the control of chaos. Secondly, allowance is made for uncertainty and emphasis is placed on the reduction rather than the suppression of chaos. The aim becomes that of confining a chaotic attractor within a prescribed region of the state space. A controller fulfilling this task is obtained as the solution of a min-max optimal control problem.

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