Robust heteroclinic networks in coupled identical cell systems and patterns of desynchronization and resynchronization along heteroclinic connections

Room M031
Thursday, 11 February, 2016 - 14:45

It is often relatively easy to identify and classify large classes of robust heteroclinic networks and cycles in certain classes of equivariant dynamics and systems governed by generalized Lotka-Volterra equations. On the other hand, there is a lack of methods for identifying and classifying heteroclinic networks in coupled identical cell systems. We describe results that enable one to transform known results about systems governed by
generalized Lotka-Volterra equations to the setting of coupled identical cell systems. As a consequence we obtain a natural realization of a large class of robust heteroclinic networks in coupled identical cell systems. We describe some of this work, what it means it terms of desynchronization and resynchronization along heteroclinic connections, and indicate one or two applications and outstanding problems.

Speaker: 

Michael Field