Transition to burst synchronization in coupled neuron networks

Transition to burst synchronization (BS), where all the neurons start and end bursting simultaneously, has been studied on a diffusively coupled network of Hindmash-Rose bursting neurons. When the coupling strength epsilon is increased from zero, spatiotemporal chaos can be first tamed into one type of BS states with fold-homoclinic bursting, which then undergoes spike-adding and transits into another type of BS states with fold-Hopf bursting. The latter transition takes place via dynamic cluster separation, during which all the neurons with degree k>k(c) change to show fold-Hopf bursting, with epsilon k(c) nearly a constant. A reasonable mechanism behind such phenomena is given by using local mean field approximation, and the role of network topology is also discussed. The case when the neurons are coupled via chemical synapses is also briefly discussed.