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Noise-induced basin hopping in a vibro-impact system

Author

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  • de Souza, Silvio L.T.
  • Batista, Antonio M.
  • Caldas, Iberê L.
  • Viana, Ricardo L.
  • Kapitaniak, Tomasz

Abstract

The dynamics of vibro-impact systems of engineering interest is numerically studied by means of a prototype consisting of an oscillating cart containing a ball undergoing inelastic collisions with its walls. We have described a multistable regime, for which different attractors coexist with a complicated basin boundary structure in the phase space. We investigated the effect of adding a certain amount of parametric noise in this model, focusing on the basin hopping, i.e., the intermittent switching between basins of different attractors.

Suggested Citation

  • de Souza, Silvio L.T. & Batista, Antonio M. & Caldas, Iberê L. & Viana, Ricardo L. & Kapitaniak, Tomasz, 2007. "Noise-induced basin hopping in a vibro-impact system," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 758-767.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:2:p:758-767
    DOI: 10.1016/j.chaos.2005.11.056
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    References listed on IDEAS

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    1. de Souza, Sílvio L.T. & Caldas, Iberê L. & Viana, Ricardo L. & Batista, Antônio M. & Kapitaniak, Tomasz, 2005. "Noise-induced basin hopping in a gearbox model," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1523-1531.
    2. Patnaik, P.R., 2005. "Application of the Lyapunov exponent to detect noise-induced chaos in oscillating microbial cultures," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 759-765.
    3. Rajasekar, S. & Valsakumar, M.C. & Raj, S.Paul, 1998. "Noise-induced jumps in two coupled Duffing oscillators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 417-434.
    4. Gan, Chunbiao, 2005. "Noise-induced chaos and basin erosion in softening Duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1069-1081.
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    1. de Souza, S.L.T. & Batista, A.M. & Baptista, M.S. & Caldas, I.L. & Balthazar, J.M., 2017. "Characterization in bi-parameter space of a non-ideal oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 224-231.
    2. Mandal, Sayan & Sk, Nazmul & Tiwari, Pankaj Kumar & Chattopadhyay, Joydev, 2024. "Bistability in modified Holling II response model with harvesting and Allee effect: Exploring transitions in a noisy environment," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    3. Xiong Wang & Akif Akgul & Sezgin Kacar & Viet-Thanh Pham, 2017. "Multimedia Security Application of a Ten-Term Chaotic System without Equilibrium," Complexity, Hindawi, vol. 2017, pages 1-10, November.
    4. Richter, Hendrik, 2008. "On a family of maps with multiple chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 559-571.
    5. Munmuangsaen, Buncha & Srisuchinwong, Banlue, 2018. "A hidden chaotic attractor in the classical Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 61-66.

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