Controlling chaos in a pendulum equation with ultra-subharmonic resonances

Jianping Yang and Zhujun Jing

Chaos, Solitons & Fractals, 2009, vol. 42, issue 2, 1214-1226

Abstract: Analytical and numerical results concerning control of chaos in a pendulum equation with parametric and external excitations are given by using Melnikov methods. We give the necessary conditions of chaos control with ultra-subharmonic resonances (i.e. Ω/ω=p/q,q>1,p,q are prime), where homoclinic chaos or heteroclinic chaos can be inhibited. Numerical simulations show that chaotic behavior can be converted to period-nq (n∈Z+) orbits by adjusting amplitude and phase-difference of parametric excitation, and the distribution of maximum Lyapunov exponents in parameter-plane (Ψ,β) gives the regions in which chaos can be controlled.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:42:y:2009:i:2:p:1214-1226

DOI: 10.1016/j.chaos.2009.03.035

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