31 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)1689-1692
Number of pages4
JournalPhysical Review Letters
Volume84
Issue number8
DOIs
StatePublished - Jan 1 2000

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orbits
transition points
synchronism

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

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From generalized synchrony to topological decoherence : Emergent sets in coupled chaotic systems. / Barreto, Ernest; So, Paul; Gluckman, Bruce J.; Schiff, Steven J.

In: Physical Review Letters, Vol. 84, No. 8, 01.01.2000, p. 1689-1692.

Research output: Contribution to journalArticle

TY - JOUR

T1 - From generalized synchrony to topological decoherence

T2 - Emergent sets in coupled chaotic systems

AU - Barreto, Ernest

AU - So, Paul

AU - Gluckman, Bruce J.

AU - Schiff, Steven J.

PY - 2000/1/1

Y1 - 2000/1/1

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AB - 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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U2 - 10.1103/PhysRevLett.84.1689

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VL - 84

SP - 1689

EP - 1692

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

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