Stochastic bifurcation of pathwise random almost periodic and almost automorphic solutions for random dynamical systems. (English) Zbl 1317.37055
The paper deals with the almost periodic and the almost automorphic dynamics of a class of random dynamical systems defined by a Stratonovich stochastic differential equations with time-varying coefficients. One begins with the pitchfork bifurcation of the stochastic equation and then, later, one considers their transcritical bifurcation. The study firstly refers to the pitchfork bifurcation of a typical special non-autonomous stochastic equation, and then considers the P-bifurcation of a more general non-autonomous stochastic equation. In some instance, one can obtain the explicit form of the solution, what is helpful to establish the results.
Reviewer: Guy Jumarie (Montréal)
MSC:
| 37H20 | Bifurcation theory for random and stochastic dynamical systems |
| 37G35 | Dynamical aspects of attractors and their bifurcations |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
Keywords:
pullback attractor; random periodic solution; random almost periodic solution; random automorphic solution; stochastic bifurcationReferences:
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