Analysis of phase models for two coupled Hodgkin-Huxley neurons

Abstract

A small coupled network of physiology-based neurons provides a nice paradigm to study collective synchronous dynamics arising from mutual cooperation between nonlinear oscillators. We study a system of two identical Hodgkin-Huxley neurons with symmetric synaptic coupling and symmetric external de current input using the phase reduction method to compute the effective interaction between two phases of neurons from synaptic coupling. With the help of the phase model, we analyze phase-locking dynamics of the synchrony, the out-of-phase state, and the anti-phase state of the system, and study the transitions between them in the parameter space of the synaptic reversal potential and the time delay. The phase diagrams for phase shifts and combined firing rates computed from the phase model are found to be consistent with ones from direct numerical simulations of the full system of two weakly coupled neurons. Finally, implications of our results on cortical dynamics modeling and the validity of the phase model are discussed.