几类细胞神经网络全局指数稳定性研究

发布时间：2018-12-26 19:07

【摘要】：细胞神经网络是一种信息处理系统,其特点是细胞之间局部连接,输出函数是分段线性的。因此,它能够实现大规模非线性模拟电路信号的实时与并行处理,并提高运行速度。细胞神经网络已成功应用于优化问题、模式识别和图像处理等领域。稳定性是细胞神经网络应用于实际问题的前提。由于放大器有限的开关速度和电子元件中发生的错误,导致电子神经网络中产生时滞。而时滞常常会破坏细胞神经网络系统的稳定性,甚至导致系统产生剧烈振荡。对于时滞细胞神经网络的研究具有重要的理论价值和现实意义。借助非线性测度的方法,本文主要对几类带有时滞的细胞神经网络的全局指数稳定性进行研究,具体研究内容如下:1、研究具有多比例时滞细胞神经网络的全局指数稳定性。通过对一类带有无界时滞的微分不等式的稳定性进行研究,然后利用所得的结果,借助非线性测度方法得到该网络全局指数稳定的充分条件。2、研究具有时变时滞周期细胞神经网络的全局指数稳定性。通过非线性测度方法以及对Halanay不等式进行推广,得到其稳定的充分条件。3、对具有分布时滞周期细胞神经网络的全局指数稳定性进行研究,先得出一类具有分布时滞微分不等式的稳定性条件,结合此条件和非线性测度方法,得到网络全局指数稳定的条件。4、对具有时变时滞概周期细胞神经网络的全局指数稳定性条件进行研究,通过非线性测度方法以及利用对Halanay不等式进行概周期推广的结果,得到其稳定的一个积分平均准则。最后,不同类型的细胞神经网络的例子和相应的数值模拟被提供,以证明我们方法的有效性和结论的正确性。
[Abstract]:Cellular neural network is a kind of information processing system, which is characterized by the local connection between cells, and the output function is piecewise linear. Therefore, it can realize real-time and parallel processing of large scale nonlinear analog circuit signals, and improve the speed of operation. Cellular neural networks have been successfully applied to optimization problems, pattern recognition and image processing. Stability is the premise of the application of cellular neural networks to practical problems. Due to the limited switching speed of the amplifier and the errors in the electronic components, the delay in the electronic neural network is caused. Delay often destroys the stability of cellular neural networks and even results in severe oscillations. It has important theoretical value and practical significance for the study of delayed cellular neural networks. By means of nonlinear measure, the global exponential stability of several cellular neural networks with time delay is studied in this paper. The main contents are as follows: 1. The global exponential stability of cellular neural networks with multi-scale delay is studied. By studying the stability of a class of differential inequalities with unbounded delay, the sufficient conditions for the global exponential stability of the network are obtained by using the obtained results and the nonlinear measure method. The global exponential stability of periodic cellular neural networks with time-varying delays is studied. By means of nonlinear measure method and the extension of Halanay inequality, the sufficient conditions for its stability are obtained. 3. The global exponential stability of periodic cellular neural networks with distributed delay is studied. The stability conditions of a class of differential inequalities with distributed delay are obtained. Combined with this condition and the nonlinear measure method, the condition of global exponential stability of the network is obtained. The global exponential stability conditions of almost periodic cellular neural networks with time-varying delays are studied. By means of nonlinear measure method and the results of almost periodic generalization of Halanay inequality, an integral average criterion is obtained for its stability. Finally, examples of different types of cellular neural networks and corresponding numerical simulations are provided to verify the validity of our method and the correctness of our conclusions.
【学位授予单位】：长安大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

【参考文献】