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

Vasileios TSEROLAS; Yoshifumi SEKINE

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

Vasileios TSEROLAS, Yoshifumi SEKINE

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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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E86-A No.3 pp.678-685

Publication Date: 2003/03/01

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Type of Manuscript: PAPER

Category: Nonlinear Problems

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Vasileios TSEROLAS, Yoshifumi SEKINE, "A Minimal Modeling of Neuronal Burst-Firing Based on Bifurcation Analysis" in IEICE TRANSACTIONS on Fundamentals, vol. E86-A, no. 3, pp. 678-685, March 2003, doi: .
Abstract: 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.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/e86-a_3_678/_p

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@ARTICLE{e86-a_3_678,
author={Vasileios TSEROLAS, Yoshifumi SEKINE, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Minimal Modeling of Neuronal Burst-Firing Based on Bifurcation Analysis},
year={2003},
volume={E86-A},
number={3},
pages={678-685},
abstract={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.},
keywords={},
doi={},
ISSN={},
month={March},}

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TY - JOUR
TI - A Minimal Modeling of Neuronal Burst-Firing Based on Bifurcation Analysis
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 678
EP - 685
AU - Vasileios TSEROLAS
AU - Yoshifumi SEKINE
PY - 2003
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E86-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 2003
AB - 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.
ER -