Postinhibitory rebound delay and weak synchronization in Hodgkin-Huxley neuronal networks

Noise-induced weak synchronized oscillatory activities in a globally inhibitory coupled Hodgkin-Huxley neuronal network are studied numerically. A kind of intrinsic delay induced by the postinhibitory rebound is observed and is found to be important in determining the overall frequency of the network. Synchronization occurs in an optimal range of noise intensity with a bell-shaped curve when the inhibitory coupling strength is sufficiently strong. Comparisons with the results for the excitatory coupling are also addressed.