Bounded noise: bifurcations of random dynamical systems

Ale Jan Homburg (March 24, 2011)

Please install the Flash Plugin

Abstract

Random dynamical systems with bounded noise can have multiple stationary measures with different supports. Under variation of a parameter, such as the amplitude of the noise, bifurcations of these measures may occur. We discuss such bifurcations both in a context of random diffeomorphisms and of random differential equations.

References:

* A.J. Homburg, T. Young. Bifurcations for random differential equations with bounded noise on surfaces Topol. Methods Nonlinear Anal. 35 (2010), 77-98.
* H. Zmarrou, A.J. Homburg. Dynamics and bifurcations of random circle diffeomorphisms Discrete Contin. Dyn. Syst. Ser. B 10 (2008), 719-731.
* H. Zmarrou, A.J. Homburg. Bifurcations of stationary measures of random diffeomorphisms Ergod. Th. and Dynam. Sys. 27 (2007), 1651-1692.