From networks of unstable attractors to heteroclinic switching.
We present a dynamical system that naturally exhibits two unstable attractors that are completely enclosed by each other's basin volume. This counterintuitive phenomenon occurs in networks of pulse-coupled oscillators with delayed interactions. We analytically show that upon continuously removing a local noninvertibility of the system, the two unstable attractors become a set of two nonattracting saddle states that are heteroclinically connected. This transition equally occurs from larger networks of unstable attractors to heteroclinic structures and constitutes a new type of singular bifurcation in dynamical systems.
Kirst
Christoph
C
Network Dynamics Group, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37073 Göttingen, Germany.
Timme
Marc
M