2002/09/18 by Marc Timme, Fred Wolf, T. Geisel +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Neuroscience · Physics and Astronomy · #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #cond-mat.dis-nn #q-bio.NC #stochastic dynamics and bifurcation
paper · pdf · doi:10.1063/1.1501274
published as Chaos 13, 377 (2003); cond-mat ps version is nicer than pdf · 14 pages, 12 figures
arxiv created 2002/09/18 · openalex publication_date 2003/02/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Common experience suggests that attracting invariant sets in nonlinear dynamical systems are generally stable. Contrary to this intuition, we present a dynamical system, a network of pulse-coupled oscillators, in which unstable attractors arise naturally. From random initial conditions, groups of synchronized oscillators (clusters) are formed that send pulses alternately, resulting in a periodic dynamics of the network. Under the influence of arbitrarily weak noise, this synchronization is followed by a desynchronization of clusters, a phenomenon induced by attractors that are unstable. Perpetual synchronization and desynchronization lead to a switching among attractors. This is explained by the geometrical fact, that these unstable attractors are surrounded by basins of attraction of other attractors, whereas the full measure of their own basin is located remote from the attractor. Unstable attractors do not only exist in these systems, but moreover dominate the dynamics for large networks and a wide range of parameters.