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Analysis of Bifurcation and Chaos in Hodgkin-Huxley Model

Author: CheYanQiu
Tutor: WangJiang
School: Tianjin University
Course: Control Theory and Control Engineering
Keywords: Hodgkin-Huxley model Branch Chaos Nerve fibers External electric field
CLC: TM159
Type: Master's thesis
Year: 2005
Downloads: 254
Quote: 2
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Abstract


The electromagnetic effects of electromagnetic fields on the human body has recently received much attention , on the one hand , more and more reports on electromagnetic pathogenic ; Clinical specific electromagnetic effects of certain diseases have a certain effect . The nervous system is an important regulator of the body's physiological function , to feel external stimuli by neurons and nerve discharge to external stimuli information encoding , transmission and decoding . Different discharge patterns reflect different external stimuli , corresponding to different physiological effects . Therefore , in-depth study of the quantitative relationship between the external electromagnetic field with neural discharge mode , and make better use of more effective prevention of electromagnetic -like illness , the treatment of diseases of the electromagnetic effects have important theoretical and practical significance . Neurophysiological activity complex nonlinear dynamical behavior , Hodgkin-Huxley (HH) model for the study of the bifurcation , chaos and nonlinear dynamics theory and methods to study the effect of low-frequency external electric field with electric stimulation parameters to change the dynamic characteristics of the HH model . In this paper, the high -dimensional systems Hopf bifurcation algebraic criterion to calculate the DC current and DC electric field strength of single- parameter bifurcation parameter and two-parameter bifurcation points ( set ) , the range of system parameters stable periodic solution exists . DC stimulation of nerve fibers in different discharge patterns correspond to the parameters given simulation interval . Chaos theory , the variation of the system under of cyclical current and periodic electrical field stimulation nerve fiber discharge mode , the emphasis on the the discharge mode frequency specificity ; found in the nerve fiber discharge mode contains periodic , quasi-periodic complex nonlinear dynamics , chaos , including the behavior ; according to the study gives particular stimulus intensity discharge mode frequency range , electromagnetic environmental standards formulation , clinical applications of electromagnetic fields have certain guiding significance .

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