Global asymptotic coherence in discrete dynamical systems

Proceedings of the National Academy of Sciences of the United States of America
David J D Earn, S A Levin

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 multispecies 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.

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Citations

Apr 29, 2010·Journal of Mathematical Biology·C Connell McCluskey, David J D Earn
Oct 16, 2007·Bulletin of Mathematical Biology·Bradley G Wagner, David J D Earn
Sep 1, 2009·Journal of Biological Dynamics·Igor BelykhSergio Rinaldi
Aug 2, 2013·Journal of the Royal Society, Interface·Adam Lampert, Alan Hastings
Jan 26, 2010·PLoS Computational Biology·Yossi Ben ZionNadav M Shnerb
Jul 7, 2012·Ecology·Gur YaariDavid A Vasseur
Feb 5, 2008·The American Naturalist·Alessandro ColomboSergio Rinaldi
Jun 3, 2015·Journal of Mathematical Biology·Alfonso Ruiz-Herrera
Aug 15, 2015·Journal of Mathematical Biology·Jacques A L Silva
Feb 11, 2015·Journal of Theoretical Biology·Daniel Franco, Alfonso Ruiz-Herrera
Jan 20, 2015·Scientific Reports·Yuval R ZelnikGur Yaari
Apr 7, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·David A Kessler, Nadav M Shnerb
Sep 6, 2013·International Journal of Geriatric Psychiatry·Alexandra KönigRenaud David

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