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dc.contributor.authorAshwin, Peteren_GB
dc.contributor.authorAston, Philip J.en_GB
dc.contributor.authorNicol, Matthewen_GB
dc.contributor.departmentUniversity of Exeter (at the time of publication Peter Ashwin was at the University of Surrey); University of Surrey; UMIST, Manchesteren_GB
dc.date.accessioned2008-03-19T16:21:20Zen_GB
dc.date.accessioned2011-01-25T10:33:19Zen_GB
dc.date.accessioned2013-03-20T12:29:38Z
dc.date.issued1998-06-18en_GB
dc.description.abstractSuppose a chaotic attractor A in an invariant subspace loses stability on varying a parameter. At the point of loss of stability, the most positive Lyapunov exponent of the natural measure on A crosses zero at what has been called a ‘blowout’ bifurcation. We introduce the notion of an essential basin of an attractor A. This is the set of points x such that accumulation points of the sequence of measures 1∕n ∑ n – 1k = 0 δfk(x) are supported on A. We characterise supercritical and subcritical scenarios according to whether the Lebesgue measure of the essential basin of A is positive or zero. We study a drift-diffusion model and a model class of piecewise linear mappings of the plane. In the supercritical case, we find examples where a Lyapunov exponent of the branch of attractors may be positive (‘hyperchaos’) or negative, depending purely on the dynamics far from the invariant subspace. For the mappings we find asymptotically linear scaling of Lyapunov exponents, average distance from the subspace and basin size on varying a parameter. We conjecture that these are general characteristics of blowout bifurcations.en_GB
dc.identifier.citationVol. 111 (1-4), pp. 81-95en_GB
dc.identifier.doi10.1016/S0167-2789(97)80006-1en_GB
dc.identifier.urihttp://hdl.handle.net/10036/21195en_GB
dc.language.isoenen_GB
dc.publisherElsevieren_GB
dc.titleOn the unfolding of a blowout bifurcationen_GB
dc.typeArticleen_GB
dc.date.available2008-03-19T16:21:20Zen_GB
dc.date.available2011-01-25T10:33:19Zen_GB
dc.date.available2013-03-20T12:29:38Z
dc.identifier.issn0167-2789en_GB
dc.descriptionCopyright © 1998 Elsevier. NOTICE: This is the author’s version of a work accepted for publication by Elsevier. Changes resulting from the publishing process, including peer review, editing, corrections, structural formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Physica D, Vol 111, Issues 1-4, 1998, DOI:10.1016/S0167-2789(97)80006-1en_GB
dc.identifier.journalPhysica Den_GB


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