Phase synchronization of inhibitory bursting neurons induced by distributed time delays in chemical coupling

Considering the fact that signal transmission time delays between different pairs of synaptically coupled neurons in the brain are different, we study the effects of distributed time delays on phase synchronization of bursting neurons. We consider the case of inhibitory coupled bursting Hindmarsh-Rose neurons and find that distributed time delays in chemical coupling can induce a variety of phase-coherent dynamic behaviors. The critical mean time delay for the emergence of coherent behaviors is inversely proportional to both the coupling strength and the average degree. This phenomenon is robust to nonidentical external inputs and is independent of network topology. A physical theory is formulated to explain the emergence of coherent neuronal activity.