# American Institute of Mathematical Sciences

August  2015, 35(8): 3745-3769. doi: 10.3934/dcds.2015.35.3745

## Stochastic bifurcation of pathwise random almost periodic and almost automorphic solutions for random dynamical systems

 1 Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM 87801

Received  May 2014 Revised  December 2014 Published  February 2015

In this paper, we introduce concepts of pathwise random almost periodic and almost automorphic solutions for dynamical systems generated by non-autonomous stochastic equations. These solutions are pathwise stochastic analogues of deterministic dynamical systems. The existence and bifurcation of random periodic (random almost periodic, random almost automorphic) solutions have been established for a one-dimensional stochastic equation with multiplicative noise.
Citation: Bixiang Wang. Stochastic bifurcation of pathwise random almost periodic and almost automorphic solutions for random dynamical systems. Discrete & Continuous Dynamical Systems, 2015, 35 (8) : 3745-3769. doi: 10.3934/dcds.2015.35.3745
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