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Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15206, U.S.A.
Department of Mathematics and Center for BioDynamics, Boston University, Boston, MA 02215, U.S.A.
We analyze the existence and stability of phase-locked states of neurons coupled electrically with gap junctions. We show that spike shape and size, along with driving current (which affects network frequency), play a large role in which phase-locked modes exist and are stable. Our theory makes predictions about biophysical models using spikes of different shapes, and we present simulations to confirm the predictions. We also analyze a large system of all-to-all coupled neurons and show that the splay-phase state can exist only for a certain range of frequencies.
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