基于映射的平均耦合神经元簇放电机理

发布时间：2018-05-12 13:58

本文选题：Rulkov神经元 + 平均耦合　；参考：《北京交通大学》2011年硕士论文

【摘要】：神经元在大脑中枢神经系统中对信息进行加工、处理起着关键的作用,神经元信息的产生和传输体现了丰富的非线性特征.研究表明,神经元在外部刺激下会产生不同的放电模式,例如周期的峰放电和簇放电,混沌的簇放电和峰放电,而在整个神经元系统中,神经脉冲的传递往往需要至少两个神经元通过耦合的方式来完成,因此耦合神经元系统是一个非常复杂的高维非线性动力系统,研究神经元系统的非线性特征能为实验提供重要的参考和依据. 本文首先引入单个Rulkov神经元模型,讨论了单个神经元产生锥形簇放电、方形簇放电及峰放电的非线性动力学特征,详细分析了锥形簇放电的放电规律和动力学特征,指出产生锥形簇放电的关键在于鞍结点分岔和flip分岔,属于fold/flip型簇放电,而锥形簇放电的持续距离随着控制参数的增加而增大.首次给出了单个神经元产生各种簇放电的参数取值范围. 其次,讨论了平均耦合神经元模型在相同的初值和不同初值条件下的簇放电机理,指出在相同的初值条件下,平均耦合的神经元不仅会产生锥形簇放电,方形簇放电和峰放电,也会产生两种三角形簇放电,并首次讨论了三角形簇放电的产生机理,得到了各种簇放电的产生条件,并用主稳定函数的方法对其稳定性做了进一步分析.当各个神经元的初值不同时,随着耦合强度的改变各个神经元之间会产生不同的簇放电和同步现象,当耦合强度为正时,会产生方形的同相同步的簇放电；当耦合强度为负时,则会产生椭圆形的反相同步的簇放电. 最后,对本文的研究内容进行了总结,为全面、完整地讨论离散神经元模型丰富的簇放电模式奠定了基础.
[Abstract]:Neurons play a key role in processing and processing information in the central nervous system of the brain. The generation and transmission of neuronal information reflect rich nonlinear characteristics. It has been shown that neurons under external stimuli produce different discharge patterns, such as periodic peak discharge and cluster discharge, chaotic cluster discharge and peak discharge, while in the whole neuron system, The transmission of neural pulses often requires at least two neurons to be coupled, so the coupled neuron system is a very complex nonlinear dynamic system with high dimension. Studying the nonlinear characteristics of neuron system can provide important reference and basis for experiment. In this paper, a single Rulkov neuron model is introduced to discuss the nonlinear dynamic characteristics of conical cluster discharge, square cluster discharge and peak discharge, and the discharge law and dynamic characteristics of cone cluster discharge are analyzed in detail. It is pointed out that the key to generate conical cluster discharge is saddle node bifurcation and flip bifurcation, which belong to fold/flip type cluster discharge, and the continuous distance of conical cluster discharge increases with the increase of control parameters. For the first time, the range of parameters for the discharge of various clusters produced by a single neuron is given. Secondly, the cluster discharge mechanism of the average coupled neuron model under the same initial value and different initial value is discussed. It is pointed out that under the same initial value, the average coupled neuron will not only produce conical cluster discharge, square cluster discharge and peak discharge. The generation mechanism of triangular cluster discharge is discussed for the first time, and the generation conditions of various cluster discharge are obtained. The stability of the cluster discharge is further analyzed by the method of principal stability function. When the initial values of each neuron are different, with the change of the coupling intensity, different cluster discharge and synchronization will occur among the neurons. When the coupling intensity is positive, there will be a square synchronous cluster discharge, and when the coupling intensity is negative, the cluster discharge will occur. An elliptical reverse phase synchronous cluster discharge will be produced. Finally, the research content of this paper is summarized, which lays a foundation for a comprehensive and complete discussion of the abundant cluster discharge model of discrete neuron model.
【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2011
【分类号】：R35

【共引文献】