NONTRIVIAL COLLECTIVE BEHAVIOR IN COUPLED MAP LATTICES - A TRANSFER OPERATOR PERSPECTIVE

Authors
CHATE H LOSSON J
Citation
H. Chate et J. Losson, NONTRIVIAL COLLECTIVE BEHAVIOR IN COUPLED MAP LATTICES - A TRANSFER OPERATOR PERSPECTIVE, Physica. D, 103(1-4), 1997, pp. 51-72
Citations number
31
Categorie Soggetti
Mathematical Method, Physical Science",Physics,"Physycs, Mathematical
Journal title
Physica. D → ACNP
ISSN journal
01672789
Volume
103
Issue
1-4
Year of publication
1997
Pages
51 - 72
Database
ISI
SICI code
0167-2789(1997)103:1-4<51:NCBICM>2.0.ZU;2-G
Abstract
We discuss the link between the presence of non-trivial collective beh avior in coupled map lattices, and the spectral properties of their tr ansfer (or Perron-Frobenius) operator. In particular, it is argued tha t non-trivial collective behavior corresponds to a Perron-Frobenius op erator possessing a cyclical spectral decomposition known as asymptoti c periodicity. We also discuss to what extent changes in the spectral properties of the Perron-Frobenius operator are related to the phase t ransitions observed between two types of non-trivial collective behavi or.