07 October 2025 , Tuesday, 14:15, in seminar room J2.138
Title:
Heteroclinic Structures: Dynamics and Stability
Abstract:
A heteroclinic connection is a solution trajectory of a dynamical system that lies in the intersection of the stable and unstable manifolds of two invariant objects. In the past decades heteroclinic structures have been studied as potential attractors in various systems with "stop-and-go" behaviour, where the system remains near a stationary state for a long time, followed by a rapid transition towards a different state. These structures can display an intricate range of stability and attraction properties tied to different dynamical phenomena. In order to understand a heteroclinic network it is often desirable to first understand its substructures — typically smaller networks or heteroclinic cycles. We discuss several notions of non-asymptotic stability and present some results in this context. Recently, the concept of an omnicycle has gained more and more attention: a periodic sequence of nodes and connections in a network where nodes and/or connections may appear multiple times. Stability of these objects is linked to switching dynamics on (parts of) the initial network. Finally, we comment on the problem of designing a heteroclinic network from a given directed graph.