具有脉冲效应的耦合反应扩散神经网络的无源性与同步

发布时间：2018-01-30 11:48

本文关键词： 耦合反应扩散神经网络无源性同步时变时滞脉冲控制　出处：《天津工业大学》2017年硕士论文　论文类型：学位论文

【摘要】：近年来,由于脉冲控制技术较低的控制成本,己经被广泛地应用于复杂网络的同步控制问题。显然,利用脉冲控制方法研究耦合反应扩散神经网络的同步问题也是非常有意义的。不幸的是,目前这方面的研究结果还非常少。另一方面,由于无源性可以使系统保持内部稳定,已经被应用于许多不同的领域,如信号处理、稳定性、复杂性、混沌控制与同步、模糊控制等。据我们所知,目前具有脉冲效应的耦合反应扩散神经网络的无源性还没有被考虑过。因此,本文分别研究了具有脉冲效应的耦合反应扩散神经网络的无源性问题以及耦合反应扩散神经网络的脉冲控制同步,其主要如下:1.具有脉冲效应的耦合反应扩散神经网络的无源性通过构造合适的李雅普诺夫泛函,利用矩阵论、图论以及一些不等式技术,我们分别建立了一些含时变时滞和不含时变时滞的脉冲型耦合反应扩散神经网络的输入、输出严格无源性的准则。最后,通过两个数值例子验证了所得到的具有脉冲效应的耦合反应扩散神经网络的无源性条件的正确性。2.耦合反应扩散神经网络的脉冲控制同步利用李雅普诺夫泛函方法、脉冲时滞微分不等式以及比较原理等方法和技术,我们建立了若干保证耦合反应扩散神经网络的全局指数同步准则。此外,我们还估计了指数收敛率,发现其依赖于时滞、系统参数和脉冲间隔。最后,我们通过数值例子说明了理论结果的正确性和有效性。
[Abstract]:In recent years, pulse control technology has been widely used in the synchronization control of complex networks due to its low control cost. It is also very meaningful to study the synchronization problem of coupled reaction diffusion neural networks by using pulse control method. Unfortunately, there are very few results in this field at present. On the other hand. As passive systems can keep internal stability, they have been used in many different fields, such as signal processing, stability, complexity, chaos control and synchronization, fuzzy control and so on. At present, the passivity of coupled reactive diffusion neural networks with pulse effect has not been considered. In this paper, the passive problem of coupled reactive diffusion neural networks with impulsive effect and pulse control synchronization of coupled reactive diffusion neural networks are studied respectively. The main results are as follows: 1. The passivity of coupled reaction-diffusion neural networks with impulsive effects by constructing appropriate Lyapunov Functionals, using matrix theory, graph theory and some inequality techniques. We establish some input and output criteria of impulsive coupled reaction-diffusion neural networks with and without time-varying delays respectively. Finally. Two numerical examples are given to verify the correctness of the passive condition of coupled reaction diffusion neural network with pulse effect. 2. Pulse control of coupled reaction diffusion neural network synchronizes the use of Lyapunov pan. Functional method. Some global exponential synchronization criteria for coupled reaction-diffusion neural networks are established by means of impulsive delay differential inequalities and comparison principles. In addition, we estimate the exponential convergence rate. It is found that it depends on time delay, system parameters and impulsive intervals. Finally, we demonstrate the correctness and validity of the theoretical results by numerical examples.
【学位授予单位】：天津工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP183

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