Synchronization in Pulse-Coupled Networks of Bursting Neurons

We study the influence of coupling strength and network topology on synchronization behavior in pulse-coupled networks of bursting neurons. We find that the stability of the completely synchronous state in networks of coupled Hindmarsh-Rose neurons only depends on the number of signals each neuron receives, independent from all other details of the network topology. This is in contrast with linearly coupled bursting neurons where complete synchrony strongly depends on the network structure and number of cells. Through analysis and numerics, we show that the onset of synchrony in a network with any coupling topology admitting complete synchronization is ensured by one single condition.