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Basins of attraction changes by amplitude constraining of oscillators with limited power supply

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  • de Souza, S.L.T.
  • Caldas, I.L.
  • Viana, R.L.
  • Balthazar, J.M.
  • Brasil, R.M.L.R.F.

Abstract

We investigate the dynamics of a Duffing oscillator driven by a limited power supply, such that the source of forcing is considered to be another oscillator, coupled to the first one. The resulting dynamics come from the interaction between both systems. Moreover, the Duffing oscillator is subjected to collisions with a rigid wall (amplitude constraint). Newtonian laws of impact are combined with the equations of motion of the two coupled oscillators. Their solutions in phase space display periodic (and chaotic) attractors, whose amplitudes, especially when they are too large, can be controlled by choosing the wall position in suitable ways. Moreover, their basins of attraction are significantly modified, with effects on the final state system sensitivity.

Suggested Citation

  • de Souza, S.L.T. & Caldas, I.L. & Viana, R.L. & Balthazar, J.M. & Brasil, R.M.L.R.F., 2005. "Basins of attraction changes by amplitude constraining of oscillators with limited power supply," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1211-1220.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:4:p:1211-1220
    DOI: 10.1016/j.chaos.2005.02.039
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    Cited by:

    1. Blazejczyk-Okolewska, Barbara & Czolczynski, Krzysztof & Kapitaniak, Tomasz, 2009. "Dynamics of a two-degree-of-freedom cantilever beam with impacts," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1991-2006.
    2. 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.
    3. Lyu, Xiaohong & Zhu, Xifeng & Gao, Quanfu & Luo, Guanwei, 2020. "Two-parameter bifurcations of an impact system under different damping conditions," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    4. Figueiredo, Annibal & Rocha Filho, Tarcisio M., 2009. "Basins of attraction of invariant regular manifolds," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1877-1889.

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