Classification of Bursting Mappings

(2004) International Journal of Bifurcation and Chaos, vol.14,n.11, 3847-3854

Eugene M. Izhikevich and Frank C. Hoppensteadt

Abstract. When a system's activity alternates between a resting state (e.g, a stable equilibrium) and an active state (e.g., a stable periodic orbit), the system is said to exhibit bursting behavior. We use bifurcation theory to classify all possible topological mechanisms of such behavior in two-dimensional mappings having one fast and one slow variable: We show that there are exactly 20 distinct types of such bursters, and that various bursters can interact, synchronize, and process information differently. Our study suggests that bursting mappings do not occur only in a few isolated examples, rather they are robust nonlinear phenomena.

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