Dephasing and Bursting in Coupled Neural Oscillators

Usually, diffusive coupling of nonlinear oscillators in one dynamical variable leads to synchronization of oscillators. We study a model of coupled neural oscillators in which simple diffusive coupling in voltage, counterintuitively, leads to dephasing of oscillators. We examine the general conditions under which dephasing through diffusive interaction will occur. We show that such systems with dephasing limit cycles lead to a new burstinglike behavior: oscillators switch between high and low oscillation amplitude. This occurs because the interaction is such that oscillators tend to synchronize for sufficiently small oscillation amplitude, while they tend to desynchronize once their oscillation amplitude has become large.