Berlin 2008 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 9: Nonlinear dynamics, synchronization and chaos I
DY 9.5: Vortrag
Montag, 25. Februar 2008, 18:00–18:15, MA 004
From Unstable Attractors to Heteroclinic Switching — •Christoph Kirst1,2,3,4 and Marc Timme1,2 — 1Network Dynamics Group, Max Planck Institute for Dynamics and Self-Organization (MPIDS) — 2Bernstein Center for Computational Neuroscience (BCCN) Göttingen, 37073 Göttingen, Germany — 3Fakultät für Physik, Georg-August-Universität Göttingen, Germany — 4DAMTP, Centre for Mathematical Sciences, Cambridge University, Cambridge CB3 0WA, UK
We report the first example of a dynamical system that naturally exhibits two unstable (Milnor) attractors that are completely enclosed by each others basin volume. This counter-intuitive phenomenon occurs in networks of pulse-coupled oscillators with delayed interactions. We analytically and numerically investigate this phenomenon and clarify the mechanism underlying it [1]: Upon continuously removing the non-invertibility of the system, the set of two unstable attractors becomes a set of two non-attracting saddle states that are heteroclinically connected to each other. This transition from a network of unstable attractors to a heteroclinic cycle constitutes a new type of bifurcation in dynamical systems.
C. Kirst and M. Timme, arXiv:0709.3432 (2007)