From Generalized Synchrony to Topological Decoherence: Emergent Sets in Coupled Chaotic Systems

Details From Generalized Synchrony to Topological Decoherence: Emergent Sets in Coupled Chaotic Systems From Generalized Synchrony to Topological Decoherence: Emergent Sets in Coupled Chaotic Systems

1999-12-07

arxiv.org/abs/chao-dyn/9912010v1

Nonlinear Sciences

Chaotic Dynamics

To appear in Physical Review Letters

Scientific paper

10.1103/PhysRevLett.84.1689

We consider the evolution of the unstable periodic orbit structure of coupled chaotic systems. This involves the creation of a complicated set outside of the synchronization manifold (the emergent set). We quantitatively identify a critical transition point in its development (the decoherence transition). For asymmetric systems we also describe a migration of unstable periodic orbits that is of central importance in understanding these systems. Our framework provides an experimentally measurable transition, even in situations where previously described bifurcation structures are inapplicable.

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