Synchrony and clustering in two and three synaptically coupled Hodgkin-Huxley neurons with a time delay

Synchrony and clustering in phase dynamics of two and three Hodgkin-Huxley neurons coupled globally by excitatory synapses with a time delay have been studied by numerical simulations and bifurcation analysis. In particular, we have obtained phase diagrams for the synchronous state and various cluster states in the parameter space of the synaptic coupling strength, G(syn), and the synaptic time delay, tau(d), by computing the phase shifts of action potential spikes. In the weak coupling limit the computed phase diagrams are found to be consistent with the results of phase model analysis. The bifurcation analysis shows the phase model predictions break down at G(syn) similar to 0.3 and new complex phase dynamics appear. For all numbers of neurons explored, the critical time delay at which the nature of synaptic coupling changes completely is found to be typically about 2-4 msec, which may have some implications in modeling cortical dynamics.