Synchronization and Clustering in a Network of Three Globally Coupled Neural Oscillators

Abstract

Collective dynamics of three globally coupled Hodgkin–Huxley neurons with a symmetric synaptic coupling has been studied as a paradigm of one of the simplest but nontrivial example of physiology-based coupled oscillator networks capable of displaying synchrony and clustering. Rich phase dynamics have been observed and the phase diagram for various phase states, in particular the synchronized state and clustered states, have been constructed by direct numerical simulations of the full system. We find that the computed phase diagram in the synaptic parameter space of the reversal potential and the signal propagation time delay reveals a rich bifurcation structure and agrees with one from bifurcation analysis of the reduced phase model. Implication of our findings in connection with two-coupled neurons and larger neural networks is discussed.