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Transition between tonic spiking and bursting in a neuron model via the blue-sky catastrophe
Andrey Shilnikov1, Gennady Cymbalyuk
1Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia 30303, USA.
Abstract:
We study a continuous and reversible transition between periodic tonic spiking and bursting activities in a neuron model. It is described as the blue-sky catastrophe, which is a homoclinic bifurcation of a saddle-node periodic orbit of codimension one. This transition constitutes a biophysically plausible mechanism for the regulation of burst duration that increases with no bound like 1/square root alpha-alpha0 as the transition value alpha0 is approached.
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