Bifurcation From Networks of Unstable Attractors to Heteroclinic Switching
| dc.creator | Kirst, Christoph | |
| dc.creator | Timme, Marc | |
| dc.date | 2007-09-21 | |
| dc.date | 2008-12-09 | |
| dc.date.accessioned | 2026-07-07T12:09:54Z | |
| dc.date.available | 2026-07-07T12:09:54Z | |
| dc.description | We present a dynamical system that naturally exhibits two unstable 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: 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. | |
| dc.description | 4 pages, 3 Figures | |
| dc.identifier | https://arxiv.org/abs/0709.3432 | |
| dc.identifier | http://arxiv.org/abs/0709.3432 | |
| dc.identifier | C. Kirst and M. Timme, Phys. Rev. E 065201(R) (2008) | |
| dc.identifier | doi:10.1103/PhysRevE.78.065201 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/209785 | |
| dc.subject | Chaotic Dynamics | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.subject | Adaptation and Self-Organizing Systems | |
| dc.subject | Neurons and Cognition | |
| dc.title | Bifurcation From Networks of Unstable Attractors to Heteroclinic Switching | |
| dc.type | text |