Theoretical Research on Bifurcation Characteristics of Hodgkin-Huxley Neuron System
Abstract: In this paper, by using the coupling Hodgkin-Huxley (HH) neural model, the bifurcation characte-ristic of neurons affected by noise, coupling strength, as well as system scale, is studied by com-puter simulation. It is found that, on the one hand, in the coupling system with certain scale and coupling strength, the bifurcation current of neurons may decrease with the increasing strength of noise, and this indicates that the appropriate noise can improve the response ability to the external weak signal. On the other hand, the bifurcation point will increase with the coupling strength, while will reduce with the increase of the number of coupling units. These indicate that the appropriate system scale and coupling strength are beneficial to the transmission of information. A better understanding of bifurcation characteristics is helpful to understand the regulation and internal mechanism of these factors on the dynamics of the system. The results will provide new insights for understanding the complex functions of the brain neural network and the relationship between the pathology and the state of the brain.
文章引用: 高 升 , 张季谦 , 谢朔俏 , 张健生 , 黄守芳 (2017) Hodgkin-Huxley神经元体系分岔特性的理论研究。 生物物理学， 5， 17-23. doi: 10.12677/BIPHY.2017.53003
Zhang, J.Q., Huang, S.F., Pang, S.T., Wang, M.S. and Gao, S. (2015) Synchronization in the Uncoupled Neuron System. Chinese Physics Letters, 12, 9-13.
 Zhang, J.Q., Huang, S.F., Pang, S.T. and Wang, M.S. (2016) Response Ability to External Signal Enhanced by Biological Spatial Configuration in Coupled HR Neural System. Chinese Journal of Chemical Physics, 27, 265-270.
Wang, P. and Zhang, J.Q. (2010) In and Anti-Transition of Firing Patterns Induced by Random Long-Range Connections in Coupled Hindmarsh-Rose Neurons System. Chinese Journal of Chemical Physics, 23, 23-29.
Wang, P. and Zhang, J.Q. and Ren, H.L. (2010) Transition of Firing Patterns in a Complex Neural Network. Scholarly Research Exchange, 2010, 1-6.
 Huang, S.F., Zhang, J.Q. and Ding, S.J. (2009) State-to-State Transitions in a Hindmarsh-Rose Neuron System. Chinese Journal of Chemical Physics, 26, 29-32.
Tanabe, S.J. and Pakdaman, K. (2001) Noise-Induced Transition in Excitable Neuron Models. Biological Cybernetics, 85, 269-280.
 Takahata, T., Tanabe, S. and Pakdaman, K. (2002) White-Noise Stimulation of the Hodgkin-Huxley Model. Biological Cybernetics, 86, 403-417.
Zhang, J.Q., Liu, J.Q. and Chen, H.S. (2008) Selective Effects of Noise by Stochastic Multi-Resonance in Coupled Cells System. Science in China Series G, 51,492-498.
 Zhang, J.Q. and Chen, H.S. (2008) Enhanced Synchronization of Intercellular Calcium Oscillations by Noise Contaminated Signals. Communications in Number Theory and Physics, 50, 903-906.
 王业遒, 张季谦, 斯小琴, 汪春道, 张恒贵. (2011) 噪声对窦房结体系钠通道电导作用的计算机仿真研究[J]. 生物物理学报, 2011, 27(5): 443-452.
 Hodgkin, A.L. and Huxley, A.F. (1952) A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve. Journal of physiology, 117, 500-544.
 Pankratova, E.V., Polovinkin, A.V. and Mosekilde, E. (2005) Resonant Activation in a Stochastic Hodgkin-Huxley Model, Interplay between Noise and Suprathreshold Driving Effects. European Physical Journal B, 45, 391-397.
Zhang, S.Y., Deng, Z.C. and Li, W.C. (2007) A Precise Runge-Kutta Integration and Its Application for Solving Nonlinear Dynamical Systems. Applied Mathematics and Computation, 184, 496-502.