CSDC Seminar: Exotic behaviour near heteroclinic networks

A heteroclinic network is a type of solution to a dynamical system consisting of a set of equilibrium solutions and connecting orbits between them. Heteroclinic networks can be thought of as an embedding of a directed graph into the phase space of the dynamical system, where vertices correspond to equilibria and directed edges to heteroclinic trajectories. The dynamics near a heteroclinic network is characterized by intermittent behaviour: solutions spend a long period of time close to one equilibrium before rapidly switching to another. The manner in which the transitions between equilibria occur can be incredibly rich: trajectories may visit all the equilibria in the network, or only a subset of them; the order in which equilibria are visited may be regular, or apparently chaotic. In spatially extended systems (modelled by partial differential equations), solutions near heteroclinic networks can arise as travelling or spiral waves.

In this talk I will present some results demonstrating this exotic behaviour near heteroclinic networks, and discuss some of the ways in which we are able to analyse this behaviour.

Visit supported by an LMS Scheme 2 grant.