Coupled cell networks: patterns of synchrony

Manuela Aguiar

November 19, 2019

A coupled cell system is a dynamical system distributed over the nodes (cells) of a network.Each cell is an individual dynamical system (which we are going to assume continuous)and the coupling structure of the network indicates the interactions between those cell dynamics. One of the key aspects in the theory of coupled cell networks concerns the existence of synchrony subspaces – subspaces defined in terms of equalities between cell coordinates which are flow-invariant. Synchrony subspaces, or patterns of synchrony, can have a major impact on both global and local dynamics and are important from the point of view of the study of that dynamics. Surprisingly, the patterns of synchrony of a network are independent of the specific individual dynamics at the nodes and are determined only by the network structure. That is, all the coupled cell systems admissible by a given network structure share the same structure of patterns of synchrony. In my talk, I will review recent concepts and results concerning patterns of synchrony in coupled cell networks.
The talk includes joint work with Ana Dias (University of Porto).