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

Ernest Barreto, Paul So, Bruce J. Gluckman, and Steven J. Schiff
Phys. Rev. Lett. 84, 1689 – Published 21 February 2000
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Abstract

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.

  • Received 10 May 1999

DOI:https://doi.org/10.1103/PhysRevLett.84.1689

©2000 American Physical Society

Authors & Affiliations

Ernest Barreto*, Paul So, Bruce J. Gluckman, and Steven J. Schiff

  • Departments of Physics & Astronomy and Psychology and the Krasnow Institute for Advanced Study, George Mason University, Fairfax, Virginia 22030

  • *Web address: http://complex.gmu.edu

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Vol. 84, Iss. 8 — 21 February 2000

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