American Institute of Mathematical Sciences

Advanced
2003, 2003(Special): 554-562. doi: 10.3934/proc.2003.2003.554

Phase-locking in electrically coupled non-leaky integrate-and-fire neurons

Timothy J. Lewis 1,

1. 

Center for Neural Science and Courant Institute of Mathematical Sciences, New York University, 4 Washington Place, Rm 809, New York, NY 10003, United States

Received  September 2002 Revised  March 2003 Published  April 2003

The synchronization properties of a pair of oscillating spiking neurons connected by electrical (diffusive) coupling is considered. The intrinsic behavior of the cells is described by the non-leaky integrate-and-fire model with a simple modification to account for the effect of spikes. Dynamics of the two-cell system are reduced to the consideration of a one-dimensional map. Periodic orbits of the map correspond to phase-locked solutions of the paired-cell system. The bifurcation structure of the map and therefore the phase-locked states in the two-cell system are analyzed. It is shown that increasing the effect of the spikes and increasing the intrinsic frequency of the cells promote synchronous activity. However, in some conditions, increasing the strength of electrical coupling can counter-intuitively lead to the destabilization of synchronous activity and the stabilization of the anti-phase state.
Keywords: Integrate-and-fire., Phase-locking, Electrical Coupling.
Mathematics Subject Classification: Primary: 92C20, 92C30; Secondary: 34A4.
Citation: Timothy J. Lewis. Phase-locking in electrically coupled non-leaky integrate-and-fire neurons. Conference Publications, 2003, 2003 (Special) : 554-562. doi: 10.3934/proc.2003.2003.554
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