Phase Dynamics for Weakly Coupled Hodgkin-Huxley Neurons

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Abstract
Hodgkin-Huxley model neurons coupled by weak excitatory interactions are studied by a phase reduction technique. All the information about the coupling between the neurons and their synchronization is then contained in an effective interaction between their phases. One shows analytically that an excitatory coupling can result in an effective inhibition between the neurons reducing their firing rates. Systems of two neurons exhibit bistability and out-of-phase locking. It is suggested that these features may have significant consequences for networks.