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Synchronisation and Extreme Value Theory for Coupled Map Lattices

Coupled Map Lattices (CML) are discrete time and space dynamical systems often used as simplified models for the study of spatially-extended non-linear systems. In the simplest “uncoupled” case, a variable defines the state of each lattice site and evolves independently in time via a non-linear map. More generally, the system evolution includes coupling between lattice sites, making for much richer possible dynamics. Previous research has explored many choices for the local map and the nature of coupling, finding dynamics including spatial chaos, stable periodic points and synchronization.

In a new paper, LML Fellow Davide Faranda and colleagues exploit Extreme Value Theory in the analysis of synchronization events in one class of chaotic coupled map lattices. A synchronization event involves the temporary close synchrony of the variables for all the lattice sites. Because nearly all trajectories of this system are recurrent, synchronization cannot last indefinitely. The authors instead investigate the probability of first synchronization, and derive results the distribution of the number of successive synchronization events when the systems evolves up to a certain time.

The paper is available at http://iopscience.iop.org/article/10.1088/1361-6544/aabc8e/meta or https://arxiv.org/pdf/1708.00191.pdf

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