Waves in Diffusively Coupled Bursting Cells

We analyze the dynamics of a spatially extended system with bistability between a homogeneous stationary state and an unstable fixed point surrounded by an oscillatory state. We show that a wave front extinguishes homogeneous oscillations, replacing them with unsteady oscillations. A traveling wave solution connects the unsteady oscillations to the stationary state. The difference in potentials of the fixed points alone determines the velocity of the wave-front fixed points. We apply our results to a generic model of neuronal bursting. [S0031-9007(99)08785-2]