Open AccessThe twofold influence of non-periodic force on chaos control
Author(s) -
Xiaoli Yang,
Wei Xu
Publication year - 2009
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.58.3722
Subject(s) - lyapunov exponent , attractor , duffing equation , control of chaos , chaotic , physics , synchronization of chaos , van der pol oscillator , nonlinear system , statistical physics , scaling , poincaré map , bounded function , chaotic hysteresis , bifurcation , control theory (sociology) , mathematical analysis , mathematics , quantum mechanics , computer science , control (management) , artificial intelligence , geometry
The influences of a kind of non-periodic forcemodeled by bounded noise or chaotic drivingon chaos control of nonlinear dynamical system are studied. Suppressing chaos as well as inducing chaos in a periodically driven Duffing-van der Pol oscillator with 5 nonlinear components is studied in detail. By examining the separation distancethe largest Lyapunov exponentthe scaling exponent of power spectrum, and the Poincar map of the considered oscillatorit is found that the non-periodic driving of appropriate amplitudeon one handcan eliminate the sensitive dependence on initial conditionsthen suppress the chaotic behavior and convert a chaotic attractor to a strange but nonchaotic one in this DVP oscillator. On the other handit can induce the chaotic behavior and then convert a periodic attractor to a chaotic one as well. Thusthe dual roles of non-periodic drivingi.e. suppressing and inducing chaosin chaos control of nonlinear dynamical systems are revealed.