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Transition to chaos in the self-excited system with a cubic double well potential and parametric forcing

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  • Litak, Grzegorz
  • Borowiec, Marek
  • Syta, Arkadiusz
  • Szabelski, Kazimierz

Abstract

We examine the Melnikov criterion for a global homoclinic bifurcation and a possible transition to chaos in case of a single degree of freedom nonlinear oscillator with a symmetric double well nonlinear potential. The system was subjected simultaneously to parametric periodic forcing and self-excitation via negative damping term. Detailed numerical studies confirm the analytical predictions and show that transitions from regular to chaotic types of motion are often associated with increasing the energy of an oscillator and its escape from a single well.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:chsofr:v:40:y:2009:i:5:p:2414-2429
    DOI: 10.1016/j.chaos.2007.10.041
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Cao, Hongjun, 2005. "Primary resonant optimal control for homoclinic bifurcations in single-degree-of-freedom nonlinear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1387-1398.
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