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On the occurrence of chaos in a parametrically driven extended Rayleigh oscillator with three-well potential

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  • Siewe, M. Siewe
  • Cao, Hongjun
  • Sanjuán, Miguel A.F.

Abstract

We examine the chaotic behavior of an extended Rayleigh oscillator in a three-well potential under additive parametric and external periodic forcing for a specific parameter choice. By applying Melnikov method, we obtain the condition for the existence of homoclinic and heteroclinic chaos. The numerical solution of the system using a fourth-order Runge–Kutta method confirms the analytical predictions and shows that the transition from regular to chaotic motion is often associated with increasing the energy of an oscillator. An analysis of the basins of attraction showing fractal patterns is also carried out.

Suggested Citation

  • Siewe, M. Siewe & Cao, Hongjun & Sanjuán, Miguel A.F., 2009. "On the occurrence of chaos in a parametrically driven extended Rayleigh oscillator with three-well potential," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 772-782.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:2:p:772-782
    DOI: 10.1016/j.chaos.2008.03.013
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    References listed on IDEAS

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    1. Jing, Zhujun & Yang, Zhiyan & Jiang, Tao, 2006. "Complex dynamics in Duffing–Van der Pol equation," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 722-747.
    2. Yang, Xiaoli & Xu, Wei & Sun, Zhongkui & Fang, Tong, 2005. "Effect of bounded noise on chaotic motion of a triple-well potential system," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 415-424.
    3. Cao, Hongjun & Seoane, Jesús M. & Sanjuán, Miguel A.F., 2007. "Symmetry-breaking analysis for the general Helmholtz–Duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 197-212.
    4. Litak, Grzegorz & Syta, Arkadiusz & Borowiec, Marek, 2007. "Suppression of chaos by weak resonant excitations in a non-linear oscillator with a non-symmetric potential," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 694-701.
    5. Jing, Zhujun & Huang, Jicai & Deng, Jin, 2007. "Complex dynamics in three-well duffing system with two external forcings," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 795-812.
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