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dc.contributor.authorAshwin, Peteren_GB
dc.contributor.authorRucklidge, Alastair M.en_GB
dc.contributor.authorSturman, Roben_GB
dc.contributor.departmentUniversity of Exeter; University of Leedsen_GB
dc.date.accessioned2008-03-13T12:05:01Zen_GB
dc.date.accessioned2011-01-25T10:33:48Zen_GB
dc.date.accessioned2013-03-20T12:31:12Z
dc.date.issued2004en_GB
dc.description.abstractNonergodic attractors can robustly appear in symmetric systems as structurally stable cycles between saddle-type invariant sets. These saddles may be chaotic giving rise to "cycling chaos." The robustness of such attractors appears by virtue of the fact that the connections are robust within some invariant subspace. We consider two previously studied examples and examine these in detail for a number of effects: (i) presence of internal symmetries within the chaotic saddles, (ii) phase-resetting, where only a limited set of connecting trajectories between saddles are possible, and (iii) multistability of periodic orbits near bifurcation to cycling attractors. The first model consists of three cyclically coupled Lorenz equations and was investigated first by Dellnitz et al. [Int. J. Bifurcation Chaos Appl. Sci. Eng. 5, 1243–1247 (1995)]. We show that one can find a "false phase-resetting" effect here due to the presence of a skew product structure for the dynamics in an invariant subspace; we verify this by considering a more general bi-directional coupling. The presence of internal symmetries of the chaotic saddles means that the set of connections can never be clean in this system, that is, there will always be transversely repelling orbits within the saddles that are transversely attracting on average. Nonetheless we argue that "anomalous connections" are rare. The second model we consider is an approximate return mapping near the stable manifold of a saddle in a cycling attractor from a magnetoconvection problem previously investigated by two of the authors. Near resonance, we show that the model genuinely is phase-resetting, and there are indeed stable periodic orbits of arbitrarily long period close to resonance, as previously conjectured. We examine the set of nearby periodic orbits in both parameter and phase space and show that their structure appears to be much more complicated than previously suspected. In particular, the basins of attraction of the periodic orbits appear to be pseudo-riddled in the terminology of Lai [Physica D 150, 1–13 (2001)].en_GB
dc.identifier.citation14 (3), pp. 571-582en_GB
dc.identifier.doi10.1063/1.1769111en_GB
dc.identifier.urihttp://hdl.handle.net/10036/20632en_GB
dc.language.isoenen_GB
dc.publisherAmerican Institute of Physicsen_GB
dc.relation.urlhttp://link.aip.org/link/?cha/14/571en_GB
dc.subjectchaosen_GB
dc.subjectbifurcationen_GB
dc.subjectstabilityen_GB
dc.subjectset theoryen_GB
dc.subjectnonlinear dynamical systemsen_GB
dc.subjectconvectionen_GB
dc.titleCycling chaotic attractors in two models for dynamics with invariant subspacesen_GB
dc.typeArticleen_GB
dc.date.available2008-03-13T12:05:01Zen_GB
dc.date.available2011-01-25T10:33:48Zen_GB
dc.date.available2013-03-20T12:31:12Z
dc.identifier.issn1054-1500en_GB
dc.descriptionCopyright © 2004 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Chaos 14 (2004) and may be found at http://link.aip.org/link/?cha/14/571en_GB
dc.identifier.journalChaosen_GB


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