随机耦合时滞反应扩散系统的同步问题

发布时间：2018-05-19 03:40

本文选题：随机耦合反应扩散系统 + 时滞　；参考：《哈尔滨工业大学》2017年硕士论文

【摘要】：复杂网络是由大量互相联系的动力节点构成的耦合系统,其在互联网、全球经济市场、社交网络以及生态系统等诸多领域有着广泛的应用。复杂网络同步现象的研究具有十分重要的理论和实际应用价值。在大多数实际系统中,系统状态会随着时间和空间的改变而变化,因此扩散作用是不能避免的。此外,时滞、随机干扰是常见的自然现象。随机耦合时滞反应扩散系统充分考虑了上述因素,因而能够更精确地模拟自然界中事物的变化规律。本文以此为视角,研究了随机耦合时滞反应扩散系统的同步问题。首先,本文介绍了随机耦合时滞反应扩散系统的研究背景与意义,并且对国内外研究现状进行分析。然后,利用边界控制的方法分别研究了随机耦合时滞反应扩散系统的随机渐近同步与均方H无穷同步。对随机耦合时滞反应扩散系统的随机渐近同步的控制问题,通过构造适当的Lyapunov泛函,应用Schur补引理等,分别针对Neumann边界条件与混合边界条件,设计了不同的边界控制器,得到了确保系统实现随机渐近同步的线性矩阵不等式形式的充分条件。当系统受到外部加性噪声干扰时,分别针对带有Neumann边界以及混合边界条件的随机耦合时滞反应扩散系统,设计不同的边界控制器,得到了确保系统实现均方H无穷同步的充分条件。最后,针对随机耦合时滞脉冲反应扩散系统,分别研究了均方有限时间同步和均方H无穷同步。关于均方有限时间同步,通过构造合适的Lyapunov-Krasovskii泛函,基于有界脉冲间隔的方法,利用Gronwall不等式等,得到系统实现有限时间同步的依赖于脉冲频率、脉冲强度、系统系数和时滞的充分条件。当系统受到外部加性噪声干扰时,得到系统实现均方H无穷同步的条件,并且指出空间区域大小对同步的影响。此外,本文通过数值算例验证了所得理论结果。
[Abstract]:Complex network is a coupling system composed of a large number of interconnected power nodes. It has been widely used in many fields such as Internet, global economic market, social network and ecosystem. The research of complex network synchronization has important theoretical and practical application value. In most real systems, the state of the system changes with time and space, so diffusion is inevitable. In addition, time delay and random disturbance are common natural phenomena. The stochastic coupled time-delay reaction-diffusion system fully considers the above factors, so it can more accurately simulate the changing law of things in nature. In this paper, the synchronization problem of stochastic coupled delay reaction-diffusion systems is studied from this perspective. Firstly, this paper introduces the research background and significance of stochastic coupled delay reaction-diffusion systems, and analyzes the current research situation at home and abroad. Then, the stochastic asymptotic synchronization and mean-square H-infinite synchronization of stochastic coupled reaction-diffusion systems with time-delay are studied by using the boundary control method, respectively. For stochastic asymptotically synchronous control of stochastic coupled reaction-diffusion systems with time-delay, different boundary controllers are designed for Neumann boundary conditions and mixed boundary conditions by constructing appropriate Lyapunov functional and applying Schur complementary Lemma. Sufficient conditions for the form of linear matrix inequalities (LMIs) to ensure the stochastic asymptotic synchronization of the systems are obtained. When the system is disturbed by external additive noise, different boundary controllers are designed for stochastic coupled delay reaction-diffusion systems with Neumann boundary conditions and mixed boundary conditions, respectively. Sufficient conditions are obtained to ensure the realization of mean square H infinite synchronization. Finally, the mean square finite time synchronization and mean square H infinite synchronization are studied for stochastic coupled delay impulsive reaction-diffusion systems. With regard to the mean square finite time synchronization, by constructing appropriate Lyapunov-Krasovskii functional, based on the bounded pulse interval method, using Gronwall inequality and so on, it is obtained that the realization of finite time synchronization depends on the pulse frequency and intensity. Sufficient conditions for system coefficients and delays. When the system is disturbed by external additive noise, the condition of realizing mean square H infinite synchronization is obtained, and the influence of space region size on synchronization is pointed out. In addition, the theoretical results are verified by numerical examples.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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