【摘要】 本文利用拓扑度理论、Liapunov泛函和时延不等式的方法研究了具有时滞的Cohen Grossberg神经网络模型dui(t)dt =ai(ui(t) )bi(ui(t) ) - ∑nj=1Tijfj(uj(t-τj) ) ,i=1 ,2 ,… ,n平衡点的稳定性问题 .文章给出了判定模型平衡点存在唯一性和全局渐近稳定性及全局指数稳定性的几个充分条件 ,这些条件取消了权矩阵 (Tij) n×n 对称性的假设 ,推广了已知文献的一些结果 ,使模型的应用范围更加广泛 .更多还原

【Abstract】 In this paper,the stability of equilibrum point of Cohen-Grossberg neural networks model with delay of the formdu i(t)dt=a i(u i(t))b i(u i(t))-∑nj=1T ijf j(u j(t-τ j)),i=1,2,…,nis investigated.By making use of the theory of topological degree,Liapunov functional method and delay differential inequality,some sufficient conditions for existence and uniqueness of equilibrum,global asymptotic stability and global exponential stability of the delay Cohen-Grossberg neural networks are obtained.These conditions are established without assuming any symmetry of the connection matrix of (T ij) n×n,thus the existed results are generalized,and the delay Cohen-Grossberg neural networks can be more widely used.更多还原