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Stochastic response analysis of noisy system with non-negative real-power restoring force by generalized cell mapping method

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Abstract

The stochastic response of a noisy system with non-negative real-power restoring force is investigated. The generalized cell mapping (GCM) method is used to compute the transient and stationary probability density functions (PDFs). Combined with the global properties of the noise-free system, the evolutionary process of the transient PDFs is revealed. The results show that stochastic P-bifurcation occurs when the system parameter varies in the response analysis and the stationary PDF evolves from bimodal to unimodal along the unstable manifold during the bifurcation.

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Authors and Affiliations

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, 710072, China

    Qun Han, Wei Xu & Xiaole Yue

Authors
  1. Qun Han
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  2. Wei Xu
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  3. Xiaole Yue
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Corresponding author

Correspondence to Qun Han.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11172233, 11302169, 11302170, and 11472212) and the Fundamental Research Funds for the Central Universities (No. 3102014JCQ01079)

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Han, Q., Xu, W. & Yue, X. Stochastic response analysis of noisy system with non-negative real-power restoring force by generalized cell mapping method. Appl. Math. Mech.-Engl. Ed. 36, 329–336 (2015). https://doi.org/10.1007/s10483-015-1918-6

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  • DOI: https://doi.org/10.1007/s10483-015-1918-6

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