A sufficient condition for bifurcation in random dynamical systems
Xiaopeng Chen, Jinqiao Duan, Xinchu Fu
TL;DR
This paper establishes a sufficient condition for bifurcation points in random dynamical systems using properties of the random Conley index, supported by examples demonstrating stochastic bifurcation phenomena.
Contribution
It introduces a new sufficient condition for bifurcation in both discrete and continuous random dynamical systems based on the random Conley index.
Findings
Properties of random Conley index are characterized.
A sufficient condition for bifurcation points is formulated.
Examples illustrate stochastic bifurcation phenomena.
Abstract
Some properties of random Conley index are obtained and then a sufficient condition for the existence of abstract bifurcation points for both discrete-time and continuous-time random dynamical systems is presented. This stochastic bifurcation phenomenon is demonstrated by a few examples.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Stability and Controllability of Differential Equations