Slow switching in a population of delayed pulse-coupled oscillators
arXiv:cond-mat/0305458 · doi:10.1103/PhysRevE.68.021919
Abstract
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.
11 pages, 8 figures, submitted to Phys. Rev. E
References in corpus (1)
Cited by in corpus (11)
- Mathematical frameworks for oscillatory network dynamics in neuroscience
- Entrainment of randomly coupled oscillator networks by a pacemaker
- Formation of feedforward networks and frequency synchrony by spike-timing-dependent plasticity
- Synchronization Engineering: Theoretical Framework and Application to Dynamical Clustering
- Strong Effects of Network Architecture in the Entrainment of Coupled Oscillator Systems
- Self-organization of feedforward structure and entrainment in excitatory neural networks with spike-timing-dependent plasticity
- Resonance Clustering in Globally Coupled Electrochemical Oscillators with External Forcing
- Clustering in Globally Coupled Oscillators Near a Hopf Bifurcation: Theory and Experiments
- Effects of non-resonant interaction in ensembles of phase oscillators
- Partial synchronization of relaxation oscillators with repulsive coupling in autocatalytic integrate-and-fire model and electrochemical experiments
- Heteroclinic cycles and chaos in a system of four identical phase oscillators with global biharmonic coupling