A Minimal Modeling of Neuronal Burst-Firing Based on Bifurcation Analysis

Vasileios TSEROLAS  Yoshifumi SEKINE  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E86-A    No.3    pp.678-685
Publication Date: 2003/03/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Nonlinear Problems
BVP model,  bursting phenomena,  nonlinear equation,  bifurcation analysis,  neural networks,  

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We propose a minimal model of neuronal burst-firing that can be considered as a modification and extention of the Bonhoeffer-van der Pol (BVP) model. By using linear stability analysis we show that one of the equilibrium points of the fast subsystem is a saddle point which divides the phase plane into two regions. In one region all phase trajectories approach a limit cycle and in the other they approach a stable equilibrium point. The slow subsystem describes a slowly varying inward current. Various types of bursting phenomena are presented by using bifurcation analysis. The simplicity of the model and the variety of firing modes are the biggest advantages of our model with obvious applications in understanding underlying mechanisms of generation of neuronal firings and modeling oscillatory neural networks.