Browsing Mathematics by Author "Rucklidge, Alastair M."
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Cycling chaos: its creation, persistence and loss of stability in a model of nonlinear magnetoconvection
Ashwin, Peter; Rucklidge, Alastair M. (Elsevier, 1998)We examine a model system where attractors may consist of a heteroclinic cycle between chaotic sets; this `cycling chaos' manifests itself as trajectories that spend increasingly long periods lingering near chaotic invariant ... 
Cycling chaotic attractors in two models for dynamics with invariant subspaces
Ashwin, Peter; Rucklidge, Alastair M.; Sturman, Rob (American Institute of Physics, 2004)Nonergodic attractors can robustly appear in symmetric systems as structurally stable cycles between saddletype invariant sets. These saddles may be chaotic giving rise to "cycling chaos." The robustness of such attractors ... 
Infinities of stable periodic orbits in systems of coupled oscillators
Ashwin, Peter; Rucklidge, Alastair M.; Sturman, Rob (American Physical Society, 2002)We consider the dynamical behavior of coupled oscillators with robust heteroclinic cycles between saddles that may be periodic or chaotic. We differentiate attracting cycles into types that we call phase resetting and free ... 
Phase resetting effects for robust cycles between chaotic sets
Ashwin, Peter; Field, Michael; Rucklidge, Alastair M.; Sturman, Rob (American Institute of Physics, 2003)In the presence of symmetries or invariant subspaces, attractors in dynamical systems can become very complicated, owing to the interaction with the invariant subspaces. This gives rise to a number of new phenomena, including ... 
Twostate intermittency near a symmetric interaction of saddlenode and Hopf bifurcations: a case study from dynamo theory
Ashwin, Peter; Rucklidge, Alastair M.; Sturman, Rob (Elsevier, 2004)We consider a model of a Hopf bifurcation interacting as a codimension 2 bifurcation with a saddlenode on a limit cycle, motivated by a loworder model for magnetic activity in a stellar dynamo. This model consists of ...