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arXiv · 1811.05354

Bifurcation in mean phase portraits for stochastic dynamical systems with multiplicative Gaussian noise

Hui Wang·Athanasios Tsiairis·Jinqiao Duan
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Abstract

We investigate the bifurcation phenomena for stochastic systems with multiplicative Gaussian noise, by examining qualitative changes in mean phase portraits. Starting from the Fokker-Planck equation for the probability density function of solution processes, we compute the mean orbits and mean equilibrium states. A change in the number or stability type, when a parameter varies, indicates a stochastic bifurcation. Specifically, we study stochastic bifurcation for three prototypical dynamical systems (i.e., saddle-node, transcritical, and pitchfork systems) under multiplicative Gaussian noise, and have found some interesting phenomena in contrast to the corresponding deterministic counterparts.

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Hui Wang, Athanasios Tsiairis, Jinqiao Duan. 2018-11-02. Bifurcation in mean phase portraits for stochastic dynamical systems with multiplicative Gaussian noise. https://arxiv.org/abs/1811.05354

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