SYNCHRONIZATION AND CLUSTERING IN A NETWORK OF 3 GLOBALLY COUPLED NEURAL OSCILLATORS

Collective dynamics of three globally coupled Hodgkin-Huxley neurons w ith a symmetric synaptic coupling has been studied as a paradigm of on e of the simplest but nontrivial example of physiology-based coupled o scillator networks capable of displaying synchrony and clustering. Ric h phase dynamics have been observed and the phase diagram for various phase states, in particular the synchronized state and clustered state s, have been constructed by direct numerical simulations of the full s ystem. We find that the computed phase diagram in the synaptic paramet er space of the reversal potential and the signal propagation time del ay reveals a rich bifurcation structure and agrees with one from bifur cation analysis of the reduced phase model. Implication of our finding s in connection with two-coupled neurons and larger neural networks is discussed.