Mechanism of bistability: Tonic spiking and bursting in a neuron model

Andrey Shilnikov, Ronald L. Calabrese, and Gennady Cymbalyuk
Phys. Rev. E 71, 056214 – Published 31 May 2005

Abstract

Neurons can demonstrate various types of activity; tonically spiking, bursting as well as silent neurons are frequently observed in electrophysiological experiments. The methods of qualitative theory of slow-fast systems applied to biophysically realistic neuron models can describe basic scenarios of how these regimes of activity can be generated and transitions between them can be made. Here we demonstrate that a bifurcation of a codimension one can explain a transition between tonic spiking behavior and bursting behavior. Namely, we argue that the Lukyanov-Shilnikov bifurcation of a saddle-node periodic orbit with noncentral homoclinics may initiate a bistability observed in a model of a leech heart interneuron under defined pharmacological conditions. This model can exhibit two coexisting types of oscillations: tonic spiking and bursting, depending on the initial state of the neuron model. Moreover, the neuron model also generates weakly chaotic bursts when a control parameter is close to the bifurcation values that correspond to homoclinic bifurcations of a saddle or a saddle-node periodic orbit.

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  • Received 30 March 2004

DOI:https://doi.org/10.1103/PhysRevE.71.056214

©2005 American Physical Society

Authors & Affiliations

Andrey Shilnikov*

  • Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia 30303, USA

Ronald L. Calabrese

  • Biology Department, Emory University, Atlanta, Georgia 30322, USA

Gennady Cymbalyuk

  • Department of Physics and Astronomy, Georgia State University, Atlanta, Georgia 30303, USA

  • *Electronic address: ashilnikov@mathstat.gsu.edu

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Vol. 71, Iss. 5 — May 2005

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