基于几何奇异摄动法研究快慢HR系统中的动力学转迁和时滞效应

发布时间：2018-03-10 08:24

本文选题：几何奇异摄动法　切入点：稳定性切换法　出处：《南昌航空大学》2016年硕士论文　论文类型：学位论文

【摘要】：Hindmarsh-Rose生物神经系统是典型的快慢系统,由于快变量和慢变量的相互作用,系统具有多种复杂的动力学现象(放电模式)。另一方面,由于信息传播和处理速度的有限性,时滞总存在于Hindmarsh-Rose生物神经系统中。本文基于几何奇异摄动理论阐述Hindmarsh-Rose系统中典型动力学现象的产生机制。首先考察系统中关键参数对系统慢变流形结构的影响,从而阐明这些参数变化时导致各种典型的动力学现象和动力学转迁的内在机制。其次,通过稳定性切换和分岔分析,发现时滞可以改变慢变流形结构,从而时滞可以改变系统的动力学行为。结合数值仿真,本文阐述了时滞导致的各种典型的动力学现象和动力学转迁过程。本文的研究将有助于进一步理解生物神经系统中复杂的放电现象,同时也丰富了非线性科学的内容。
[Abstract]:Hindmarsh-Rose biological nervous system is a typical fast and slow system. Because of the interaction of fast and slow variables, the system has many complex dynamic phenomena (discharge mode). On the other hand, due to the limited speed of information transmission and processing, Time delay always exists in the biological nervous system of Hindmarsh-Rose. Based on the theory of geometric singularity perturbation, the mechanism of typical dynamic phenomena in Hindmarsh-Rose system is discussed in this paper. Firstly, the influence of key parameters in the system on the structure of slowly variable manifold of the system is investigated. The results show that the variation of these parameters leads to a variety of typical dynamic phenomena and the intrinsic mechanism of dynamic transition. Secondly, through stability switching and bifurcation analysis, it is found that delay can change the structure of slowly variable manifolds. So time delay can change the dynamic behavior of the system. In this paper, the typical dynamic phenomena and dynamic transition processes caused by time delay are described. The study in this paper will be helpful to further understand the complex discharge phenomena in the biological nervous system and enrich the content of nonlinear science.
【学位授予单位】：南昌航空大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O175

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