Mean-field coupling of identical expanding circle maps

Abstract

Globally coupled doubling maps are studied in this paper. In this setting and for finitely many sites, two distinct bifurcation values of the coupling strength have been identified in the literature, corresponding to the emergence of contracting directions (\cite{koiller2010coupled}) and, specifically for $N=3$ sites, to the loss of ergodicity (\cite{fernandez2014breaking}). On the one hand, we reconsider these results and provide an interpretation of the observed dynamical phenomena in terms of the synchronization of the sites. On the other hand, we initiate a new point of view which focuses on the evolution of distributions and allows to incorporate the investigation of infinitely many sites. In particular we observe phenomena in the infinite system that is analogous to the limit states of the contracting regime of $N=3$ sites.

References in corpus (4)

• High Temperature Expansions and Dynamical Systems
• Remarks on the mean field dynamics of networks of chaotic elements
• Phase transitions in a piecewise expanding coupled map lattice with linear nearest neighbour coupling
• Stochastically stable globally coupled maps with bistable thermodynamic limit

Cited by in corpus (6)

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• Symmetry breaking in a globally coupled map of four sites
• Existence of physical measures in some Excitation-Inhibition Networks