Removal, Suppression, and Control of Chaos by Nonlinear Design

Techniques to remove, suppress, and control the chaotic behavior of nonlinear systems are reviewed. Analysis of a forced damped nonlinear oscillator provides a brief overview of the relevant nonlinear dynamics of dissipative systems. Various techniques for suppression and control of chaos are then outlined, compared and contrasted. A unified mathematical notation facilitates the comparison. The successes of each strategy in numerical simulations and physical experiments are carefully noted. Their strengths and weaknesses are analyzed, and they are evaluated according to whether they employ feedback, are goal-oriented, are model-based, merely remove chaos–or truly exploit it. An elementary derivation of the important OGY control equation is supplied. Critical references provide an entry into the literature. It is argued that nonlinearity can be a real-world advantage, and it is hoped that this review will serve as summary of, and invitation to, the nascent field of nonlinear design.

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ALLEE EFFECT IN POPULATION DYNAMICS: EXISTENCE OF BREATHER-LIKE BEHAVIOR AND CONTROL OF CHAOS THROUGH DISPERSAL

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127406015854 ◽

2006 ◽

Vol 16 (07) ◽

pp. 2001-2012 ◽

Cited By ~ 3

Author(s):

DESPINA HADJIAVGOUSTI ◽

SIMOS ICHTIAROGLOU

Keyword(s):

Allee Effect ◽

Chaotic Behavior ◽

Biological Species ◽

Control Of Chaos ◽

Localized Solutions ◽

A Chain ◽

Dispersal Probability ◽

And Control ◽

Time Periodic ◽

Nonzero Probability

We consider a one-dimensional chain of identical sites, appropriate for colonization by a biological species. The dynamics at each site is subjected to the demographic Allee effect. We consider nonzero probability p of dispersal to the nearby sites and we prove, for small values of p, the existence of asymptotically stable time-periodic and space-localized solutions, such that the central site carries the vast majority of the metapopulation, while the populations at nearby sites attain very small values. We study numerically a chain of three sites, both for the case of open ends or periodic boundary conditions. We study the bifurcations leading to transition from chaotic to periodic behavior and vice-versa and note that the increase of the dispersal probability in both cases controls the chaotic behavior of the metapopulation.

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Analysis and Control of Chaos in Sheppard-Taylor DC-DC Converter

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.401-403.1596 ◽

2013 ◽

Vol 401-403 ◽

pp. 1596-1599 ◽

Cited By ~ 1

Author(s):

Chuang Bi ◽

Zheng Hang Fan ◽

Yong Xiang ◽

Jin Gang Hu

Keyword(s):

Nonlinear Dynamics ◽

Bifurcation Diagram ◽

Time Domain ◽

Chaos Control ◽

Phase Portraits ◽

Control Of Chaos ◽

Complex Behaviour ◽

Power Spectral ◽

The Stability ◽

And Control

This paper addresses the nonlinear dynamics of the Sheppard-Taylor converter to explain the complex behaviour exhibited in the converter under different practical conditions. The bifurcation diagram of the converter is generated to analyze the stability of the system. Several representative waveforms are captured from simulation to illustrate the chaos control of the converter, such as time-domain waveforms, phase portraits, Poincaré section diagrams, and power spectral diagrams.

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Nonlinear wavy phenomena into plasma: some cases of stabilization and control of chaotic behaviors

Journal of Plasma Physics ◽

10.1017/s0022377811000079 ◽

2011 ◽

Vol 77 (5) ◽

pp. 679-692 ◽

Cited By ~ 4

Author(s):

CONSTANTINE L. XAPLANTERIS ◽

ELENI FILIPPAKI

Keyword(s):

Nonlinear Dynamics ◽

Experimental Study ◽

Nonlinear Theory ◽

Chaotic Behavior ◽

Argon Plasma ◽

Wave Interaction ◽

Electric Signal ◽

Theoretical Justification ◽

Wave Coupling ◽

And Control

AbstractStabilities, instabilities and turbulences have always appeared into a cylindrical magnetized argon plasma. These phenomena are caused by linear or nonlinear dynamics and are interpreted with the linear or nonlinear theory accordingly. In this paper, an experimental study accompanied by theoretical justification and based on the wave–wave interaction has been made; an azimuthally moved driving wave is enforced in a very simple way. The turbulence stabilization, the wave coupling, the instability synchronization and other wavy interactions, which are caused by using an external spatiotemporal electric signal, are presented. The research of the wavy subjects continuing in our laboratory aspires to comprehend the plasma chaotic behavior and take a step into suppressing the unstable inclination.

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