  Synchronized neural spiking is associated with many cognitive functions and
thus, merits study for its own sake. The analysis of neural synchronization
naturally leads to the study of repetitive spiking and consequently to the
analysis of coupled neural oscillators. Coupled oscillator theory thus informs
the synchronization of spiking neuronal networks. A crucial aspect of coupled
oscillator theory is the phase response curve (PRC), which describes the impact
of a perturbation to the phase of an oscillator. In neural terms, the
perturbation represents an incoming synaptic potential which may either advance
or retard the timing of the next spike. The phase response curves and the form
of coupling between reciprocally coupled oscillators defines the phase
interaction function, which in turn predicts the synchronization outcome
(in-phase versus anti-phase) and the rate of convergence. We review the two
classes of PRC and demonstrate the utility of the phase model in predicting
synchronization in reciprocally coupled neural models. In addition, we compare
the rate of convergence for all combinations of reciprocally coupled Class I
and Class II oscillators. These findings predict the general synchronization
outcomes of broad classes of neurons under both inhibitory and excitatory
reciprocal coupling.
