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Bifurcations and chaos in the triple-well Φ6-Van der Pol oscillator driven by external and parametric excitations

Author

Listed:
  • Siewe, M. Siewe
  • Kakmeni, F.M. Moukam
  • Tchawoua, C.
  • Woafo, P.

Abstract

The chaotic behavior of a nonlinear damped three-well Φ6-Van der Pol oscillator under external and parametric excitations is studied in detail by means of Melnikov's analysis. The predictions are tested against numerical simulations based on the basin of attraction of initial conditions. It is found that the threshold for the onset of chaos in the system increases as the amplitude of the parametric excitation decreases and increases as the amplitude of the external forcing increases. Additionally, the onset of chaos is studied through analysis of the Poincaré map, a construction of the bifurcation diagrams and a computation of the maximal Lyapunov exponent.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:357:y:2005:i:3:p:383-396
    DOI: 10.1016/j.physa.2005.06.070
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    Citations

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    Cited by:

    1. Ario, Ichiro, 2013. "Multiple duffing problem in a folding structure with hill-top bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 51(C), pages 52-63.
    2. Litak, Grzegorz & Borowiec, Marek & Syta, Arkadiusz & Szabelski, Kazimierz, 2009. "Transition to chaos in the self-excited system with a cubic double well potential and parametric forcing," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2414-2429.
    3. Yu, Yue & Zhang, Cong & Chen, Zhenyu & Lim, C.W., 2020. "Relaxation and mixed mode oscillations in a shape memory alloy oscillator driven by parametric and external excitations," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. Feng, Jingjing & Zhang, Qichang & Wang, Wei, 2012. "Chaos of several typical asymmetric systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(7), pages 950-958.
    5. Wu, Jianxin & Hong, Yiguang & Chen, Guanrong, 2009. "Occurrence and underlying mechanism of multi-stripe chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2250-2258.

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