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Subharmonic bifurcations and chaotic motions for a class of inverted pendulum system

Author

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  • Zhou, Liangqiang
  • Liu, Shanshan
  • Chen, Fangqi

Abstract

Using both analytical and numerical methods, global dynamics including subharmonic bifurcations and chaotic motions for a class of inverted pendulum system are investigated in this paper. The expressions of the heteroclinic orbits and periodic orbits are obtained analytically. Chaos arising from heteroclinic intersections is studied with the Melnikov method. The critical curves separating the chaotic and non-chaotic regions are obtained. The conditions for subharmonic bifurcations are also obtained. It is proved that the system can be chaotically excited through finite subharmonic bifurcations. Some new dynamical phenomena are presented. Numerical simulations are given, which verify the analytical results.

Suggested Citation

  • Zhou, Liangqiang & Liu, Shanshan & Chen, Fangqi, 2017. "Subharmonic bifurcations and chaotic motions for a class of inverted pendulum system," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 270-277.
    • Handle: RePEc:eee:chsofr:v:99:y:2017:i:c:p:270-277
    DOI: 10.1016/j.chaos.2017.04.004
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    References listed on IDEAS

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    1. Pérez-Polo, Manuel F. & Pérez Molina, Manuel & Gil Chica, Javier & Berna Galiano, José A., 2014. "Stability and chaotic behavior of a PID controlled inverted pendulum subjected to harmonic base excitations by using the normal form theory," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 698-718.
    2. Niu, Hongli & Wang, Jun, 2013. "Complex dynamic behaviors of oriented percolation-based financial time series and Hang Seng index," Chaos, Solitons & Fractals, Elsevier, vol. 52(C), pages 36-44.
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