The most probable response of some prototypical stochastic nonlinear dynamical systems

Ping Han, Wei Xu, Liang Wang and Shichao Ma

Chaos, Solitons & Fractals, 2020, vol. 132, issue C

Abstract: The response of the stochastic system hardly provides useful information for researching its characteristic. Therefore, the paper is aimed at utilizing a deterministic tool, namely, the most probable response, to explore the stochastic nonlinear system. Firstly, one defines the most probable response of the stochastic system. Then, its analytical solution is derived by incorporating the extremum theory into the associated Fokker–Planck equation. Finally, two examples are given to illustrate respectively the implication of this method. Meanwhile, it can conclude that the large the intensity of multiplicative noise is, the more obvious the impact is on the response of nonlinear system. However, no matter how the intensity of additive noise changes, the most probable response does not change. The numerical method verifies the validity of analytical solution.

Keywords: Stochastic systems; Fokker–Planck equation; The extremum theory; The most probable response (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:132:y:2020:i:c:s0960077920300114

DOI: 10.1016/j.chaos.2020.109612

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