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

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

Slow switching in globally coupled oscillators: robustness and occurrence through delayed coupling.

The phenomenon of slow switching in populations of globally coupled oscillators is discussed. This characteristic collective dynamics, which was first discovered in a particular class of the phase oscillator model, is a result of the formation of a heteroclinic loop connecting a pair of clustered states of the population. We argue that the same behavior can arise in a wider class of oscillator ...

Desynchronization of pulse-coupled oscillators with delayed excitatory coupling

Collective behavior of pulse-coupled oscillators has been investigated widely. As an example of pulse-coupled networks, fireflies display many kinds of flashing patterns. Mirollo and Strogatz (1990) proposed a pulse-coupled oscillator model to explain the synchronization of South East Asian fireflies (Pteroptyx malaccae). However, transmission delays were not considered in their model. In fact,...

Prevalence of unstable attractors in networks of pulse-coupled oscillators.

We present and analyze the first example of a dynamical system that naturally exhibits attracting periodic orbits that are unstable. These unstable attractors occur in networks of pulse-coupled oscillators, and become prevalent with increasing network size for a wide range of parameters. They are enclosed by basins of attraction of other attractors but are remote from their own basin volume suc...

Heteroclinic Switching in Coupled Oscillator Networks: Dynamics on Odd Graphs

We review some examples of dynamics displaying sequential switching for systems of coupled phase oscillators. As an illustration we discuss a simple family of coupled phase oscillators for which one can find robust heteroclinic networks between unstable cluster states. For N = 2k + 1 oscillators we show that there can be open regions in parameter space where the heteroclinic networks have the s...