Slow switching in a population of delayed pulse-coupled oscillators

Hiroshi Kori
2003 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
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
more » ... sy 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.
doi:10.1103/physreve.68.021919 pmid:14525018 fatcat:phksvkbv6jdurlxsp5ltggcgai