具反映扩散有限连续分布时滞细胞神经网络的全局指数稳定性  

Global exponential stability of distributed delays neural networks with reaction-diffusion terms

作　　者：罗毅平[1] 邓飞其[2] 汤志宏[2] 杨逢建[3] 

机构地区：[1]湖南工程学院 数理系,湖南湘潭411101 [2]华南理工大学自动化科学与工程学院,广东广州510640 [3]仲凯农业技术学院 数学系,广东广州510225

出　　处：《控制理论与应用》2007年第2期210-214,共5页Control Theory & Applications

基　　金：国家自然科学基金(60374023);湖南省自然科学基金(05JJ40093);湖南省教育厅自然科学基金重点资助项目(A04012)

摘　　要：研究了具反应扩散有限连续分布细胞神经网络的平衡点的存在性及全局指数稳定性问题,提出了新的比较原理,在对神经元的激励函数的较宽松的条件下,利用同伦不变性原理获得了该系统的平衡点的存在性,利用所得的比较原理获得了该系统全局指数渐近稳定性的充分条件,而且这些条件容易检验,并举了一个数值实例以说明结论的有效性．The existence of the equilibrium point and global exponential stability of distributed delays neural networks with reaction-diffusion terms are investigated in this paper. Firstly, a new comparative theorem is obtained. Secondly, without assuming the boundedness, monotonicity and differentiability of the activation functions, the sufficient conditions of the existence of the systems＇ equilibrium point are obtained by utilizing the theory of homotopy invariability, and the sufficient conditions of the global exponential stability of the systems with distributed delays by Dini＇s derivative, Mfunction and the new extended Halanay＇s inequality. Finally, a numerical example is given to illustrate the applicability of this condition.

关 键 词：反应扩散 连续分布时滞 平衡点 全局指数稳定性 比较原理 

分 类 号：O175.21[理学—数学]