几类时标网络模型的动力学分析

发布时间：2018-03-04 09:00

本文选题：时标　切入点：神经网络　出处：《集美大学》2017年硕士论文　论文类型：学位论文

【摘要】：近年来,随着时标理论的提出,时标动力学方程及其应用引起了各国学者的广泛关注.时标动力学方程在研究系统时更具一般性,不仅能描述连续变化过程和离散变化过程,而且可以刻画连续和离散混合的过程.因此,时标理论在金融,生物系统,复杂网络和工程应用等方面具有广泛的应用前景.然而,时标动力学理论在神经网络的应用研究相对较少,尚有很多动力学行为有待进一步研究,特别是神经网络的稳定性,多重周期性以及同步控制问题.基于前人的基础,我们引入时标上微积分理论研究了时标上神经网络的稳定性、周期解和同步性.本文分析了时标上几类网络模型的动力学性质.主要内容包括:第一部分研究了时标上含N段激活函数的一类2维神经网络的指数型周期解,获得系统存在N2个周期解并且解是指数型稳定的.第二部分研究了时标上一类简化背景神经网络的完全收敛性,证明了网络的完全收敛性,有界性和具有全局吸引集.第三部分解决了在q-容许时标上具有比例时滞的一类神经网络的同步控制问题,解决了离散条件下带比例时滞的网络的同步控制问题.
[Abstract]:In recent years, with the development of the theory of time scale, the dynamic equation of time scale and its application have attracted the attention of scholars all over the world. The dynamic equation of time scale is more general in the study of the system, and it can not only describe the continuous change process and discrete change process. Therefore, time scale theory has a wide range of applications in finance, biological systems, complex networks and engineering applications. The application of time-scale dynamics theory in neural networks is relatively few, and there are still many dynamic behaviors to be further studied, especially the stability, multiple periodicity and synchronization control of neural networks. In this paper, we introduce the calculus theory of time scale to study the stability of time scale neural network. In this paper, the dynamical properties of several network models on time scales are analyzed. The main contents are as follows: in the first part, the exponential periodic solutions of a class of two-dimensional neural networks with N segment activation function are studied. It is obtained that there are N _ 2 periodic solutions and the solutions are exponential stable. In the second part, the complete convergence of a class of simplified background neural networks on time scales is studied, and the complete convergence of the network is proved. In the third part, the synchronization control problem of a class of neural networks with proportional delay on q-admissible time scale is solved, and the synchronization control problem of a network with proportional delay under discrete conditions is solved.
【学位授予单位】：集美大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175;O231

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