神经动力学系统的稳定性分析与镇定控制

发布时间：2018-06-08 15:56

本文选题：神经动力学系统 + 忆阻　；参考：《湖北师范大学》2017年硕士论文

【摘要】：作为一类特定的动力系统,神经动力学系统模拟了现实生物神经元的结构和功能.在生物、物理及经济等各个领域都有广泛的应用,而这些应用都依赖于该系统的动态特征.因此,对神经动力学系统的动态性质进行研究是具有理论和实际意义的.本文主要研究了几类神经动力学系统.利用带有广义常数变量微分方程理论、广义Gronwall不等式、分数阶Leibniz法则、不等式技巧,结合具体的神经动力学系统,分析其动态演化特征,得到了一些神经动力学系统的理论判据.本文主要工作概述如下:讨论了一类带有延迟和超前变元的随机神经动力学系统均方指数稳定性.基于广义常数变量微分方程理论,给出了确保该类随机神经动力学系统解存在唯一的充分判据,揭示了这种动力系统在当前时刻的状态与在导向函数时刻状态之间的关系,并获得了其全局均方指数稳定性判据.探讨了一类分数阶神经动力学系统的全局Mittag-Leffler稳定性.建立了一类带有广义常数变量的分数阶神经动力学系统,通过分数阶微分方程理论,分析了该系统的动态行为.将带有广义常数变量的整数阶系统稳定性结果推广到分数阶系统中,为研究带有广义常数变元的复杂控制系统提供了新思想.探究了一类时滞分数阶忆阻神经动力学系统的全局O(t-α)镇定.基于分数阶系统的比较原理,设计了分数阶忆阻神经动力学系统的镇定控制策略,分析了系统全局O(t-α)镇定,改进了现有的一些相关结果.本文针对几类神经动力学系统的研究,特别是带有广义常数变量系统的研究,为进一步分析带有广义常数变量系统的性质奠定了基础.
[Abstract]:As a specific dynamic system, neurodynamic system simulates the structure and function of real biological neurons. It is widely used in biological, physical and economic fields, and these applications depend on the dynamic characteristics of the system. Therefore, it is of theoretical and practical significance to study the dynamic properties of neurodynamic systems. In this paper, several kinds of neurodynamic systems are studied. By using the theory of differential equation with generalized constant variables, generalized Gronwall inequality, fractional Leibniz rule, inequality technique, and combining with the specific neurodynamic system, the dynamic evolution characteristics of the equation are analyzed. Some theoretical criteria for neurodynamic systems are obtained. The main work of this paper is summarized as follows: the mean square exponential stability of a class of stochastic neurodynamic systems with delay and leading arguments is discussed. Based on the theory of generalized constant variable differential equations, a sufficient criterion is given to ensure the existence and uniqueness of the solution of this kind of stochastic neurodynamic system, and the relationship between the state of the dynamic system at the present moment and the state of the guidance function is revealed. The global mean square exponential stability criterion is obtained. The global Mittag-Leffler stability of a class of fractional order neurodynamic systems is discussed. A class of fractional order neurodynamic systems with generalized constant variables is established. The dynamic behavior of the system is analyzed by the theory of fractional differential equations. The stability results of integer order systems with generalized constant variables are extended to fractional order systems, which provides a new idea for the study of complex control systems with generalized constant arguments. In this paper, the global Ot- 伪 stabilization of a class of fractional order memory resistive neurodynamic systems with time delay is investigated. Based on the comparison principle of fractional order systems, a stabilization control strategy for fractional order amnesia neurodynamic systems is designed. The global Ot- 伪 stabilization of the systems is analyzed, and some related results are improved. In this paper, the study of several kinds of neurodynamic systems, especially the system with generalized constant variables, has laid a foundation for the further analysis of the properties of systems with generalized constant variables.
【学位授予单位】：湖北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175;O231

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