| 一类神经元模型的Hopf分岔 |
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| 引用本文： | 郑改华,梅凤翔.一类神经元模型的Hopf分岔[J].北京理工大学学报,2002,22(5):553-555. |
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| 作者姓名： | 郑改华 梅凤翔 |
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| 作者单位： | 北京理工大学,应用力学系,北京,100081 |
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| 基金项目： | 国家自然科学基金;19972010; |
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| 摘 要： | 用非线性动态系统的观点看待神经元的静息和周期放电现象.通过对神经元简化数学模型的理论分析,将神经元的静息态对应模型的稳定平衡态.神经元的神经可激活性对应模型参数处于分岔点附近,神经元的周期放电态对应模型在第1次Hopf分岔之后出现的极限环稳态,用模型的二次Hopf分岔后极限环消失及稳定的不动点重新出现说明神经过程中发生的过强抑制现象.
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| 关 键 词： | 非线性动态系统 Hopf分岔 神经元 静息态 周期放电 神经可激活性 |
| 文章编号： | 1001-0645(2002)05-0553-03 |
| 收稿时间： | 2001/11/18 0:00:00 |
The Hopf Bifurcation of a Neuron Model |
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| ZHENG Gai-hua and MEI Feng-xiang.The Hopf Bifurcation of a Neuron Model[J].Journal of Beijing Institute of Technology(Natural Science Edition),2002,22(5):553-555. |
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| Authors: | ZHENG Gai-hua and MEI Feng-xiang |
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| Institution: | Dept. of Applied Mechanics, Beijing Institute of Technology, Beijing100081, China;Dept. of Applied Mechanics, Beijing Institute of Technology, Beijing100081, China |
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| Abstract: | The theory of nonlinear dynamical system was used to describe the phenomenon of neural rest and spikes. It is shown that the quiescent state of neuron is mathematically equivalent to a stable spiral, the neural excitability is referred to a state near bifurcation, and the periodic spike is equivalent to a stable limit cycle in the Hopf bifurcation. Similarly, the phenomenon of restrain after too strong an excitation corresponds to the second Hopf bifurcation. |
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| Keywords: | nonlinear dynamical system Hopf bifurcation neuron quiescent state periodic spike neural excitiability |
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