Lattices of Synchrony Subspaces and their Indices

Hiroko Kamei, University of Dundee, will be presenting at this event.

Various synchronous behaviours, from full synchrony to partial synchrony, can be observed for a given network. We use the coupled cell network formalism to study all possible partial synchronies, which are determined solely by network structure and termed synchrony subspaces of the network. In this talk, we consider a regular network where identical individual dynamical systems (cells) are coupled with only one type of interaction. All possible synchrony subspaces have a hierarchy structure, which can be represented as a complete lattice. By assigning an nonnegative integer index to this lattice, we use the lattice structure to predict the existence of synchrony-breaking bifurcating branches of the network. We also show how the lattice structure can be reduced by identifying an equivalence relation which leads to multiple bifurcating branches from a single bifurcation point along these equivalent synchrony subspaces.

This event is part of the Leeds Applied Nonlinear Dynamics seminar series.