Transition between tonic spiking and bursting in a neuron model via the blue-sky catastrophe |
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Authors: | Shilnikov Andrey Cymbalyuk Gennady |
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Institution: | Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia 30303, USA. |
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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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