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Chaos of several typical asymmetric systems

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  • Feng, Jingjing
  • Zhang, Qichang
  • Wang, Wei

Abstract

The threshold for the onset of chaos in asymmetric nonlinear dynamic systems can be determined using an extended Padé method. In this paper, a double-well asymmetric potential system with damping under external periodic excitation is investigated, as well as an asymmetric triple-well potential system under external and parametric excitation. The integrals of Melnikov functions are established to demonstrate that the motion is chaotic. Threshold values are acquired when homoclinic and heteroclinic bifurcations occur. The results of analytical and numerical integration are compared to verify the effectiveness and feasibility of the analytical method.

Suggested Citation

  • Feng, Jingjing & Zhang, Qichang & Wang, Wei, 2012. "Chaos of several typical asymmetric systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(7), pages 950-958.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:7:p:950-958
    DOI: 10.1016/j.chaos.2012.02.022
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    References listed on IDEAS

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    1. 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.
    2. Tchoukuegno, R. & Nana Nbendjo, B.R. & Woafo, P., 2002. "Resonant oscillations and fractal basin boundaries of a particle in a φ6 potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 304(3), pages 362-378.
    3. Siewe, M. Siewe & Kakmeni, F.M. Moukam & Tchawoua, C. & Woafo, P., 2005. "Bifurcations and chaos in the triple-well Φ6-Van der Pol oscillator driven by external and parametric excitations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 357(3), pages 383-396.
    4. Sofroniou, Anastasia & Bishop, Steven R., 2006. "Breaking the symmetry of the parametrically excited pendulum," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 673-681.
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    Cited by:

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    2. Bella, Giovanni, 2017. "Homoclinic bifurcation and the Belyakov degeneracy in a variant of the Romer model of endogenous growth," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 452-460.

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