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Synchronization of coupled map lattices

Part of: Infinite-dimensional dissipative dynamical systems Time-dependent statistical mechanics (dynamic and nonequilibrium) Dynamical systems with hyperbolic behavior Smooth dynamical systems: general theory

Published online by Cambridge University Press:  30 March 2023

Alexandre Baraviera ,
Pedro Duarte  and
Maria Joana Torres
Alexandre Baraviera
Affiliation:
Instituto de Matemática e Estatística, UFRGS, Av. Bento Gonçalves 9500, Porto Alegre, RS 91500, Brazil ([email protected])
Pedro Duarte
Affiliation:
CMAF, Departamento de Matemática, Faculdade de Ciências da Universidade de Lisboa, Campo Grande, Lisboa 1749-016, Portugal ([email protected])
Maria Joana Torres
Affiliation:
CMAT and Departamento de Matemática, Universidade do Minho, Campus de Gualtar, Braga 4700-057, Portugal ([email protected])
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Abstract

In this paper, we address the issue of synchronization of coupled systems, introducing concepts of local and global synchronization for a class of systems that extend the model of coupled map lattices. A criterion for local synchronization is given; numerical experiments are exhibited to illustrate the criteria and also to raise some questions in the end of the text.

Keywords

stochastic kernelglobal/local synchronizationcoupled map latticeHardy-Littlewood maximal operatorAmari neural networkMarkov chain

MSC classification

Primary: 37C99: None of the above, but in this section
Secondary: 37D99: None of the above, but in this section 37L60: Lattice dynamics 82C20: Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 66 , Issue 1 , February 2023 , pp. 143 - 163
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.

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