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Stochastic sensitivity analysis of nonautonomous nonlinear systems subjected to Poisson white noise

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  • Sun, Yahui
  • Hong, Ling
  • Jiang, Jun

Abstract

The stochastic sensitivity function (SSF) method is extended to estimate the stationary probability distribution around periodic attractors of nonautonomous nonlinear dynamical systems subjected to Poisson white noise in this paper. After deriving the stochastic sensitivity functions of period-N cycle of mapping systems based on the characteristic of Poisson process, non-autonomous dynamical systems around periodic attractors are converted to mapping systems by constructing a stroboscopic map, and then the stochastic sensitivity functions of periodic attractors of nonautonomous nonlinear systems can be obtained by adopting the results of mapping systems. It is found that the stochastic sensitivity functions depend on the product of noise intensity and the arrival rate of Poisson processes. To illustrate the validity of the proposed method, a Henon map driven by Poisson processes and a Mathieu–Duffing oscillator under Poisson white noise are studied.

Suggested Citation

  • Sun, Yahui & Hong, Ling & Jiang, Jun, 2017. "Stochastic sensitivity analysis of nonautonomous nonlinear systems subjected to Poisson white noise," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 508-515.
    • Handle: RePEc:eee:chsofr:v:104:y:2017:i:c:p:508-515
    DOI: 10.1016/j.chaos.2017.09.014
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    References listed on IDEAS

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    1. Juan Wu & Yong Xu & Jun Ma, 2017. "Lévy noise improves the electrical activity in a neuron under electromagnetic radiation," PLOS ONE, Public Library of Science, vol. 12(3), pages 1-13, March.
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    Cited by:

    1. Irina Bashkirtseva, 2024. "Approximations in Mean Square Analysis of Stochastically Forced Equilibria for Nonlinear Dynamical Systems," Mathematics, MDPI, vol. 12(14), pages 1-12, July.
    2. Lev Ryashko & Irina Bashkirtseva, 2022. "Stochastic Bifurcations and Excitement in the ZS-Model of a Thermochemical Reaction," Mathematics, MDPI, vol. 10(6), pages 1-11, March.

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