Global asymptotic coherence in discrete dynamical systems

David J.D. Earn, Simon Asher Levin

Research output: Contribution to journalArticle

24 Scopus citations

Abstract

Spatial synchrony (coherence) in dynamical systems is of both theoretical and applied importance. We address this problem for a generalization of coupled map lattices (CMLs). In the systems we study, which we term "meta-CMLs, " the map at each lattice point may be multidimensional (corresponding, for example, to multi-species ecological systems in which all species have the same dispersal pattern). Most previous work on coherence of CMLs has focused on local stability. Here, we prove a global theorem that provides a useful sufficient condition guaranteeing decay of incoherence in meta-CMLs regardless of initial conditions and regardless of the nature of the attractors of the system. This result facilitates useful analyses of a variety of applied problems, including conservation of endangered species and eradication of pests or infectious diseases.

Original languageEnglish (US)
Pages (from-to)3968-3971
Number of pages4
JournalProceedings of the National Academy of Sciences of the United States of America
Volume103
Issue number11
DOIs
StatePublished - Mar 14 2006

All Science Journal Classification (ASJC) codes

  • General

Keywords

  • Global stability
  • Metapopulation dynamics
  • Synchronization
  • Synchrony

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