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Cognitive Neurodynamics

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01-12-2015 | Research Article

Dynamical analysis of periodic bursting in piece-wise linear planar neuron model

Authors: Ying Ji, Xiaofang Zhang, Minjie Liang, Tingting Hua, Yawei Wang

Published in: Cognitive Neurodynamics | Issue 6/2015

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Abstract

A piece-wise linear planar neuron model, namely, two-dimensional McKean model with periodic drive is investigated in this paper. Periodical bursting phenomenon can be observed in the numerical simulations. By assuming the formal solutions associated with different intervals of this non-autonomous system and introducing the generalized Jacobian matrix at the non-smooth boundaries, the bifurcation mechanism for the bursting solution induced by the slowly varying periodic drive is presented. It is shown that, the discontinuous Hopf bifurcation occurring at the non-smooth boundaries, i.e., the bifurcation taking place at the thresholds of the stimulation, leads the alternation between the rest state and spiking state. That is, different oscillation modes of this non-autonomous system convert periodically due to the non-smoothness of the vector field and the slow variation of the periodic drive as well.

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Title: Dynamical analysis of periodic bursting in piece-wise linear planar neuron model
Authors: Ying Ji
Xiaofang Zhang
Minjie Liang
Tingting Hua
Yawei Wang
Publication date: 01-12-2015
Publisher: Springer Netherlands
Published in: Cognitive Neurodynamics / Issue 6/2015
Print ISSN: 1871-4080
Electronic ISSN: 1871-4099
DOI: https://doi.org/10.1007/s11571-015-9347-z

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