Slow switching in a population of delayed pulse-coupled oscillators

Details Slow switching in a population of delayed pulse-coupled oscillators Slow switching in a population of delayed pulse-coupled oscillators

2003-05-20

arxiv.org/abs/cond-mat/0305458v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

11 pages, 8 figures, submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.68.021919

We show that peculiar collective dynamics called slow switching arises in a population of leaky integrate-and-fire oscillators with delayed, all-to-all pulse-couplings. By considering the stability of cluster states and symmetry possessed by our model, we argue that saddle connections between a pair of the two-cluster states are formed under general conditions. Slow switching appears as a result of the system's approach to the saddle connections. It is also argued that such saddle connections easy to arise near the bifurcation point where the state of perfect synchrony loses stability. We develop an asymptotic theory to reduce the model into a simpler form, with which an analytical study of cluster states becomes possible.

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