Minimal attractors and bifurcations of random dynamical systems

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Minimal attractors and bifurcations of random dynamical systems

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dc.contributor.author Ashwin, Peter en_GB
dc.contributor.department University of Exeter (at the time of publication the author was at the University of Surrey) en_GB
dc.date.accessioned 2008-04-01T16:15:38Z en_GB
dc.date.accessioned 2011-01-25T10:33:50Z en_US
dc.date.accessioned 2013-03-20T12:29:58Z
dc.date.issued 1999 en_GB
dc.description.abstract 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. en_GB
dc.identifier.citation 455 (1987), pp. 2615-2634 en_GB
dc.identifier.doi 10.1098/rspa.1999.0419 en_GB
dc.identifier.uri http://hdl.handle.net/10036/22079 en_GB
dc.language.iso en en_GB
dc.publisher Royal Society en_GB
dc.relation.url http://dx.doi.org/10.1098/rspa.1999.0419 en_GB
dc.relation.url http://publishing.royalsociety.org/index.cfm?page=1086# en_GB
dc.subject chaotic dynamics en_GB
dc.subject random dynamical systems en_GB
dc.subject forced systems en_GB
dc.subject blowout bifurcation en_GB
dc.title Minimal attractors and bifurcations of random dynamical systems en_GB
dc.type Article en_GB
dc.type Preprint en_GB
dc.date.available 2008-04-01T16:15:38Z en_GB
dc.date.available 2011-01-25T10:33:50Z en_US
dc.date.available 2013-03-20T12:29:58Z
dc.identifier.issn 1364-5021 en_GB
dc.identifier.issn 1471-2946 en_GB
dc.description Copyright © 1999 The Royal Society. NOTICE: This is the author’s version of a work accepted for publication by The Royal Society. The definitive version was subsequently published in Proceedings of the Royal Society A, Vol 455, Number 1987, 8 July 1999, DOI:10.1098/rspa.1999.0419 en_GB
dc.identifier.journal Proceedings of The Royal Society A en_GB


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