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Period-adding bifurcations and chaos in a periodically stimulated excitable neural relaxation oscillator
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
The response of an excitable neuron to trains of electrical spikes is relevant to the understanding of the neural code. In this paper we study a neurobiologically motivated relaxation oscillator, with appropriately identified fast and slow coordinates, that admits an explicit mathematical analysis. An application of geometric singular perturbation theory shows the existence of an attracting invariant manifold which is used to construct the Fenichel normal form for the system. This facilitatesdoi:10.1103/physreve.62.4057 pmid:11088930 fatcat:jlfk3sazkbfvrbcaspzsguykl4