Chaos control in a pendulum system with excitations

Xianwei Chen; Zhujun Jing; Xiangling Fu

doi:10.3934/dcdsb.2015.20.373

Article Contents

2015, Volume 20, Issue 2: 373-383. Doi: 10.3934/dcdsb.2015.20.373

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Chaos control in a pendulum system with excitations

1.
School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan, 411201
2.
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190

Received: January 2014

Revised: August 2014

Published: March 2015

Abstract / Introduction Related Papers Cited by

Abstract

This paper is devoted to investigate the problem of controlling chaos for a pendulum system with parametric and external excitations. By using Melnikov methods, the criteria of controlling chaos are obtained. Numerical simulations are given to illustrate the effect of the chaos control for this system, suppression of homoclinic chaos is more effective than suppression of heteroclinic chaos, and the chaotic motions can be suppressed to period-motions by adjusting parameters of chaos-suppressing excitation. Finally, we calculate the maximum Lyapunov exponents (LE) in parameter-plane and observe the frequency of chaos-suppressing excitation also play an important role in the process of chaos control.

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Mathematics Subject Classification: Primary: 34G20, 34H05; Secondary: 34H10.

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