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A new procedure for exploring chaotic attractors in nonlinear dynamical systems under random excitations

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Abstract

Due to uncertain push-pull action across boundaries between different attractive domains by random excitations, attractors of a dynamical system will drift in the phase space, which readily leads to colliding and mixing with each other, so it is very difficult to identify irregular signals evolving from arbitrary initial states. Here, periodic attractors from the simple cell mapping method are further iterated by a specific Poincaré map in order to observe more elaborate structures and drifts as well as possible dynamical bifurcations. The panorama of a chaotic attractor can also be displayed to a great extent by this newly developed procedure. From the positions and the variations of attractors in the phase space, the action mechanism of bounded noise excitation is studied in detail. Several numerical examples are employed to illustrate the present procedure. It is seen that the dynamical identification and the bifurcation analysis can be effectively performed by this procedure.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Zhejiang University, 310027, Hangzhou, China

    Chun-Biao Gan

  2. Institute of Applied Mechanics, SAA, Zhejiang University, 310027, Hangzhou, China

    Hua Lei

Authors
  1. Chun-Biao Gan
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  2. Hua Lei
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Correspondence to Hua Lei.

Additional information

The project was supported by the National Natural Science Foundation of China (10672140, 11072213).

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Gan, CB., Lei, H. A new procedure for exploring chaotic attractors in nonlinear dynamical systems under random excitations. Acta Mech Sin 27, 593–601 (2011). https://doi.org/10.1007/s10409-011-0472-6

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  • DOI: https://doi.org/10.1007/s10409-011-0472-6

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