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Controlling chaos in a pendulum equation with ultra-subharmonic resonances

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  • Yang, Jianping
  • Jing, Zhujun

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.

Suggested Citation

  • Yang, Jianping & Jing, Zhujun, 2009. "Controlling chaos in a pendulum equation with ultra-subharmonic resonances," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1214-1226.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:2:p:1214-1226
    DOI: 10.1016/j.chaos.2009.03.035
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    1. Yang, Jianping & Jing, Zhujun, 2008. "Inhibition of chaos in a pendulum equation," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 726-737.
    2. Alasty, Aria & Salarieh, Hassan, 2007. "Nonlinear feedback control of chaotic pendulum in presence of saturation effect," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 292-304.
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