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Reducing and Bifurcation Analyse of the Neuron Model

Author: ZhangRongHua
Tutor: WangJiang
School: Tianjin University
Course: Detection Technology and Automation
Keywords: Nervous system Reduced-order Stability Branch Central pattern generator
CLC: Q42
Type: Master's thesis
Year: 2007
Downloads: 103
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Abstract

External stimulation , the nervous system, resulting in a variety of action potential encoding , complex nonlinear dynamics . The nervous system is composed by a plurality of neurons of the neural network, to achieve the transfer and processing of the neural information . The study of neurons and their networks contribute to the understanding of brain function and acupuncture electrical signal conduction and the role of law . This paper studies the model of a single neuron reduction, simplification, and simplified neuron model of stability and bifurcation analysis . The neuron is a complex nonlinear system , with dozens dimensional equation to describe the dynamic characteristics . In this paper, a method of analysis of the nonlinear dynamics , reduced-order model of neurons , with reduced-order model of the dynamics of the neurons . Reduction neuronal model and the original model have the same characteristics , but using Reduction model can make the neural network model greatly simplified and better analysis of network characteristics . Firstly, the use of mathematical models of neurons in different free variable evolution speed , the model is reduced from fourth-order second order . Classification of neurons mathematical model based on the Izhikevich the reduced-order model classified as six a minimal model . This article in the reduced-order model based on nonlinear dynamics model . We found that by analyzing the high - threshold model has three equilibrium point in the entire phase space . But it will not happen Hopf bifurcation . Low - threshold model in the phase space is only one equilibrium point , when the applied current , leakage conductance and sodium ions back EMF changes , the model can generate a Hopf bifurcation . This study provides some ideas for the study of nerve conduction and nervous system activity .

Reducing and Bifurcation Analyse of the Neuron Model

Abstract

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