Bifurcation control of a parametric pendulum

Aline S. de Paula, Marcelo A. Savi, Marian Wiercigroch, Ekaterina Evgenievna Pavlovskaia

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

In this paper, we apply chaos control methods to modify bifurcations in a parametric pendulum-shaker system. Specifically, the extended time-delayed feedback control method is employed to maintain stable rotational solutions of the system avoiding period doubling bifurcation and bifurcation to chaos. First, the classical chaos control is realized, where some unstable periodic orbits embedded in chaotic attractor are stabilized. Then period doubling bifurcation is prevented in order to extend the frequency range where a period-1 rotating orbit is observed. Finally, bifurcation to chaos is avoided and a stable rotating solution is obtained. In all cases, the continuous method is used for successive control. The bifurcation control method proposed here allows the system to maintain the desired rotational solutions over an extended range of excitation frequency and amplitude.

Original languageEnglish
Article number1250111
Number of pages14
JournalInternational Journal of Bifurcation and Chaos
Volume22
Issue number5
DOIs
Publication statusPublished - May 2012

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