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神经元模型的复杂动力学:分岔与编码
引用本文:王海侠,陆启韶,郑艳红.神经元模型的复杂动力学:分岔与编码[J].动力学与控制学报,2009,7(4):293-296.
作者姓名:王海侠  陆启韶  郑艳红
作者单位:1. 南京理工大学理学院,南京,210094
2. 北京航空航天大学理学院,北京,100191
3. 福建师范大学数学与计算机科学学院,福州,350007
基金项目:国家自然科学基金,南京理工大学科技发展基金资助项目 
摘    要:研究了改进的Morris—Lecar(ML)神经元模型的放电节律模式和模式转化的峰峰间期(interspike intervals,ISIs)分岔结构,通过调节模型中的两个重要参数μ和Vk,发现对于固定的μ,改变Vk,神经元呈现出从倍周期级联分岔到加周期分岔的复杂结构,放电模式从静息态转化为周期、混沌簇放电状态;若选取此分岔过程中的某一Vk值,对μ进行调节,呈现出的ISIs分岔结构在很大程度上取决于单个神经元的放电节律模式,且单个神经元处于混沌簇放电时,肛带来的分岔动力学行为较丰富.由于神经元能够通过动作电位对信息进行编码,所以我们推测,研究神经元的放电节律模式和动作电位的ISIs分岔结构能为理解神经信息编码机制提供线索.

关 键 词:分岔  峰峰间期  神经编码
收稿时间:2009/5/20 0:00:00

Complex dynamics of the neuronal model: bifurcation and encoding
Wang Haixi,Lu Qishao and Zheng Yanhong.Complex dynamics of the neuronal model: bifurcation and encoding[J].Journal of Dynamics and Control,2009,7(4):293-296.
Authors:Wang Haixi  Lu Qishao and Zheng Yanhong
Affiliation:Wang Haixia1 Lu Qishao2 Zheng Yanhong3(1.School of Science,Nanjing University of Science , Technology,Nanjing 210094,China)(2.School of Science,Beihang University,Beijing 100191,China)(3.School of Mathematics , Computer Science,Fujian Normal University,Fuzhou 350007,China)
Abstract:Firing rhythm patterns and the interspike intervals (ISis) bifurcation structures of the action potential in the modified Morris - Lecar (ML) neuronal model are investigated. By modulating two important control parameters μ and Vk, we find that for some fixed μ, varying Vk, the neuron exhibits a cascade of period doubling bifurcation and period -adding bifurcation leading the system from the silent regime to a periodic and chaotic state dominated by bursting events; While,if we take some peculiar values of Vk based on the former bifurcation diagram, modulating/x can lead to a variety of bifurcation structures which have something to do with the single neuron' s firing patterns, moreover, chaotic bursting brings us much richer bifurcation dynamics than periodic bursting. We know that neurons can encode information by use of action potentials, based on this, we infer that study of firing rhythm patterns and ISis structures can be a clue to understand the mechanism of the neuronal encoding.
Keywords:bifurcation  interspike intervals (ISIs)  neuronal encoding  
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