张薇, 安新磊, 王红梅, 乔帅. mHR神经元模型的分岔分析及其哈密顿能量控制[J]. 云南大学学报(自然科学版), 2021, 43(3): 486-494. doi: 10.7540/j.ynu.20200109
引用本文: 张薇, 安新磊, 王红梅, 乔帅. mHR神经元模型的分岔分析及其哈密顿能量控制[J]. 云南大学学报(自然科学版), 2021, 43(3): 486-494. doi: 10.7540/j.ynu.20200109
ZHANG Wei, AN Xin-lei, WANG Hong-mei, QIAO Shuai. Bifurcation analysis and Hamiltonian energy control of mHR Neuron model[J]. Journal of Yunnan University: Natural Sciences Edition, 2021, 43(3): 486-494. DOI: 10.7540/j.ynu.20200109
Citation: ZHANG Wei, AN Xin-lei, WANG Hong-mei, QIAO Shuai. Bifurcation analysis and Hamiltonian energy control of mHR Neuron model[J]. Journal of Yunnan University: Natural Sciences Edition, 2021, 43(3): 486-494. DOI: 10.7540/j.ynu.20200109

mHR神经元模型的分岔分析及其哈密顿能量控制

Bifurcation analysis and Hamiltonian energy control of mHR Neuron model

  • 摘要: 研究能量函数对神经元放电特性的影响,对控制神经系统的信息编码、信息传递有着至关重要的作用. 文章运用了亥姆霍兹定理与数值仿真相结合的方法,研究了mHR神经元模型在双参数平面内的分岔行为及其放电模式的控制. 通过数值仿真发现,mHR神经元模型具有非常丰富的分岔现象,在不同的参数平面内存在倍周期分岔、逆倍周期分岔及无混沌加周期等分岔现象. 在此基础上,为了实现对神经元模型混沌放电模式的控制,对神经元系统施加了哈密顿能量反馈控制器. 研究发现,通过适当调节该控制器的参数,就能够有效地控制神经元的放电模式类型. 这对了解复杂神经元系统的能量消耗及其稳定性具有一定的现实意义.

     

    Abstract: It is very important to study the effect of external energy on the firing of neurons for controlling the information encoding and transmission in the nervous system. In this paper, the bifurcation behavior of mHR Neuron model in two parameter plane and the control of its discharge pattern are studied by using the method of Helmholtz theorem and numerical simulation. The numerical simulation shows that the mHR neural model has abundant bifurcation phenomenon, such as period-doubling bifurcation, period-doubling bifurcation and period-adding bifurcation in different parameter planes. On this foundation, in order to control the chaotic discharge pattern of the Neuron model, the Hamiltonian energy feedback controller is applied to the neuron system. It is found that by adjusting the parameters of the controller, the firing pattern of neurons can be controlled effectively. It is of practical significance to understand the energy consumption and stability of complex neuron system.

     

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