随机时滞系统的动力学行为分析

发布时间：2018-07-05 07:50

本文选题：随机捕食模型 + 全局渐近稳定性　；参考：《南昌大学》2017年硕士论文

【摘要】：本文利用Lyapunov泛函方法和随机分析理论,研究了两类随机时滞系统的动力学行为,主要工作如下:第一章介绍了随机时滞系统的研究背景、研究进展以及现实意义,同时给出了下文将要用到的相关定义和引理.第二章研究了一类带有两种不同功能函数的随机时滞一个捕食者两个竞争食饵模型,通过构造合适的Lyapunov-Krasovskii泛函,证明了系统的全局正解是存在惟一的和随机最终有界性的,进而给出了系统的随机持久性和灭绝性的充分条件,然后通过控制环境噪声强度和参数给出了模型全局渐近稳定性的充分条件,最后给出了一些数值例子进一步说明所得结论的有效性.第三章讨论了一类带有混合时滞的随机中立型忆阻神经网络模型的输入-状态稳定性问题,在模型中同时考虑了中立项和混合时滞,使得模型更具有新颖性,并且利用Lyapunov稳定性理论和随机分析理论得出了系统均方指数输入-状态稳定性的条件,最后给出一些数值例子佐证了所得结论的正确性.第四章给出了本文的结论以及对后续工作的展望.
[Abstract]:In this paper, the dynamic behavior of two kinds of stochastic time-delay systems is studied by using Lyapunov functional method and stochastic analysis theory. The main work is as follows: in Chapter 1, the background, research progress and practical significance of stochastic time-delay systems are introduced. At the same time, the relevant definitions and Lemma used in this paper are given. In chapter 2, we study a class of stochastic predator and two competitive prey models with two different function functions. By constructing appropriate Lyapunov-Krasovskii functional, we prove that the global positive solution of the system is unique and stochastic ultimate boundedness. Furthermore, the sufficient conditions for stochastic persistence and extinction of the system are given, and the sufficient conditions for the global asymptotic stability of the model are obtained by controlling the environmental noise intensity and parameters. Finally, some numerical examples are given to illustrate the validity of the conclusion. In chapter 3, we discuss the input-state stability of a class of stochastic neutral amnesia neural networks with mixed delays. We consider both neutral terms and mixed delays in the model, which makes the model more novel. By using Lyapunov stability theory and stochastic analysis theory, the conditions for the input-state stability of the mean square exponent are obtained. Finally, some numerical examples are given to prove the correctness of the conclusions. The fourth chapter gives the conclusion of this paper and the future work.
【学位授予单位】：南昌大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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