【作者】 吴爱龙；

【导师】 傅朝金；

【作者基本信息】 湖北师范学院 ， 应用数学， 2010， 硕士

【摘要】 时滞脉冲神经网络是时滞大系统的一个重要组成部分,具有十分丰富的动力学属性.鉴于它在信号处理、动态图像处理以及全局优化等问题中的重要应用,近年来,时滞脉冲神经网络的动力学问题引起了学术界的广泛关注.尤其是时滞脉冲神经网络平衡点的全局稳定性(包括全局渐近稳定性、全局指数稳定性等)得到了深入的研究,也获得了一系列深刻的结果.本文主要对一类时滞脉冲神经网络(即Hopfield神经网络)平衡点的全局渐近稳定性或全局指数稳定性进行了一系列的研究,取得了一些较深刻的结果.具体地说,本论文涉及到如下内容：(1)非Lipschitz神经元激励下时滞脉冲神经网络几乎所有现存的文献是基于Lipschitz神经元激励下研究时滞脉冲神经网络的稳定性问题.然而,很少研究非Lipschitz神经元激励下时滞脉冲神经网络的稳定性.基于此,本文主要对一类非Lipschitz神经元激励下时滞脉冲神经网络全局稳定性进行了一系列的研究,获得的一些新的结果.(2)时滞脉冲神经网络的稳定性分析运用同胚映射理论、拓扑度理论和Lyapunov泛函方法,得到了一些新的具有较少约束的全局渐近稳定性或全局指数稳定性判据,改进了现有的结果.(3)脉冲对时滞神经网络稳定性的影响针对当前许多时滞脉冲神经网络的稳定性判据均要求原时滞系统Lyapunov稳定的弊端,我们运用不等式技巧,得到了一些保证系统全局稳定的充分条件,放宽了对脉冲强度的限制,这对实际时滞脉冲系统的设计具有较强的指导作用.更多还原

【Abstract】 As an important part of the delayed large systems, the delayed neural networks with impulses may exhibit the rich and colorful dynamical behaviors. Due to their important applications in signal processing, image processing as well as optimizing problems, the dy-namical issues of delayed neural networks with impulses have attracted worldwide attention in recent years. Recently, many interesting stability criteria for the equilibriums of delayed neural networks with impulses have been derived via Lyapunov function/functional method. A series of significative results have been obtained. This thesis mainly focuses on the global stability for a type of delayed neural networks with impulse. Specifically, the main contents are as follows:(1) Non-Lipschitz Neuron Activations for Delayed Neural Networks with ImpulsesMost existing results on stability for neural networks with impulses were obtained under some special assumptions on neuron activation functions, such as Lipschitz conditions. Cor-respondingly, there is not much work dedicated to investigate the stability of neural networks with non-Lipschitz neuron activations. The objective of this thesis is to study the stability of a class of delayed impulsive neural networks with non-Lipschitz neuron activations. Our results obtained in this thesis provide new sufficient criteria for a class of delayed impulsive neural networks developed by us.(2) Stability Analysis for Delayed Neural Networks with ImpulsesSeveral novel global asymptotical stability/global exponential stability criteria with less restriction are established by employing homeomorphism theory, topological degree theory and Lyapunov functional method, our obtained criteria improves the existing result.(3) Effects of Impulses on Stability of Delayed Neural NetworksWe investigate the global stability conditions of the delayed neural networks with im-pulses by means of inequality techniques. And the results overcome the restriction that the original neural network should be Lyapunov stable. The impulsive strength or impulse inter-val can be estimated by applying the proposed results.更多还原