Synchronization for Networks of Globally Coupled Maps in the Thermodynamic Limit

Abstract We study a network of finitely many interacting clusters where each cluster is collection globally coupled circle maps in the thermodynamic (or mean field) limit. The state described by probability measure, and its evolution given self-consistent transfer operator. A synchronized if Dirac measure. provide sufficient conditions for all to synchronize we describe setups are met thanks uncoupled dynamics and/or (diffusive) nature coupling. also give partially states arise—i.e. only subset synchronized—due forcing group on rest network. Lastly, use this framework show emergence stability chimera these systems.