Browsing Mathematics by Author "Sturman, Rob"
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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 ... 
Decelerating defects and nonergodic critical behaviour in a unidirectionally coupled map lattice
Ashwin, Peter; Sturman, Rob (Elsevier, 2003)We examine a coupled map lattice (CML) consisting of an infinite chain of logistic maps coupled in one direction by inhibitory coupling. We find that for sufficiently strong coupling strength there are dynamical states ... 
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 ...