Almost-synchronous solutions for mutually coupled excitatory neurons

We consider synchronization in a pair of neurons described by voltage-gated conductance equations and coupled by mutual excitation. Our model neurons have three time scales: the very fast transition between active and inactiv e stares; an intermediate scale during the active portion of a cell's traje ctory; and the slowest during the inter-burst interval. We show that the in terplay of time scales can lead to stable "almost-synchronous" solutions in which the jumps between active and inactive states of the two cells happen with a time difference that is a small fraction of the total period of the coupled system. Furthermore, modulation of parameters not affecting time s cales can change the stable solution from almost-synchronous to synchronous . We use a geometric analysis that enables us to identify the parts of the trajectories over which the interactions move the coupled trajectory away f rom synchrony, the parameters responsible for this phenomenon and how the d istance from synchrony depends on the time scales and can be modulated. (C) 2000 Elsevier Science B.V. All rights reserved.