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Talk Abstract
Spatial Patterns in Bursting Systems

John Hunter, Univ. of Califonia, Davis

Spatial pattern formation in bursting systems can be modeled by systems of reaction diffusion equations with weak diffusive coupling. We study a simple two by two model of bursting systems in which stable limit cycle oscillations coexist with a stable steady state. This system combines features of oscillatory media and bistable media with two stable steady states. A natural question for such systems concerns the spatial propagation of "phase boundaries" between oscillatory, bursting states and stable steady states. Numerical computations and supporting analysis show a rather surprising behavior: a spatial wave extinguishes the oscillatory state and replaces it with an unstable steady state. The unstable steady state is connected to the stable steady state by a travelling wave.

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