The response analysis of fractional-order stochastic system via generalized cell mapping method

Liang Wang, Lili Xue, Chunyan Sun, Xiaole Yue, Wei Xu

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16 引用 (Scopus)

摘要

This paper is concerned with the response of a fractional-order stochastic system. The short memory principle is introduced to ensure that the response of the system is a Markov process. The generalized cell mapping method is applied to display the global dynamics of the noise-free system, such as attractors, basins of attraction, basin boundary, saddle, and invariant manifolds. The stochastic generalized cell mapping method is employed to obtain the evolutionary process of probability density functions of the response. The fractional-order 6 oscillator and the fractional-order smooth and discontinuous oscillator are taken as examples to give the implementations of our strategies. Studies have shown that the evolutionary direction of the probability density function of the fractional-order stochastic system is consistent with the unstable manifold. The effectiveness of the method is confirmed using Monte Carlo results.

源语言英语
文章编号013118
期刊Chaos
28
1
DOI
出版状态已出版 - 1 1月 2018

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