University of Surrey

Test tubes in the lab Research in the ATI Dance Research

Minimal attractors and bifurcations of random dynamical systems

Ashwin, Peter (1999) Minimal attractors and bifurcations of random dynamical systems 455. pp. 2615-2634.


Download (237kB)


We consider attractors for certain types of random dynamical systems. These are skew-product systems whose base transformations preserve an ergodic invariant measure. We discuss definitions of invariant sets, attractors and invariant measures for deterministic and random dynamical systems. Under assumptions that include, for example, iterated function systems, but that exclude stochastic differential equations, we demonstrate how random attractors can be seen as examples of Milnor attractors for a skew-product system. We discuss the minimality of these attractors and invariant measures supported by them. As a further connection between random dynamical systems and deterministic dynamical systems, we show how dynamical or D-bifurcations of random attractors with multiplicative noise can be seen as blowout bifurcations, and we relate the issue of branching at such D-bifurcations to branching at blowout bifurcations.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Ashwin, Peter
Date : 8 July 1999
Additional Information : Published in ,i>Proceedings of the Royal Society of London A</i>, <i>455</i>, 2615-2634. © 1999 The Royal Society.
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:41
Last Modified : 31 Oct 2017 14:02

Actions (login required)

View Item View Item


Downloads per month over past year

Information about this web site

© The University of Surrey, Guildford, Surrey, GU2 7XH, United Kingdom.
+44 (0)1483 300800