Stability of Cohen–Grossberg neural networks with unbounded distributed delays Tingwen Huang a, * , Chuandong Li b , Goong Chen c a Texas A&M University at Qatar, c/o Qatar Foundation, P.O. Box 5825, Doha, Qatar b Department of Computer Science and Engineering, Chongqing University, Chongqing 400030, PR China c Mathematics Department, Texas A&M University, College Station, TX 77843, USA Accepted 31 March 2006 Abstract In this paper, we investigate the dynamics of the Cohen–Grossberg neural networks with unbounded distributed delays. A new criteria for globally asymptotic stability of Cohen–Grossberg neural networks with distributed delays is presented. Ó 2006 Elsevier Ltd. All rights reserved. 1. Introduction The Cohen–Grossberg neural networks (CGNN) were first proposed by Cohen and Grossberg [6]. They can be described by the following equation: _ x i ðtÞ¼a i ðx i ðtÞÞ d i ðx i ðtÞÞ  X n j¼1 b ij g j ðx j ðtÞÞ " # ; i ¼ 1; ... ; n; ð1Þ where b ij denotes the connection weights; a i (x i ) and d i (x i ), i = 1, ... , n, are the amplification functions and the self-signal functions, respectively; while g j (x j ), j = 1, ... , n, are the activation functions. Model (1) has attracted many researchers to investigate its existence of equilibrium and stability. Among them, Lu and Chen [18] investigated the exponential stability of the above model. However, in reality, time delays inevitably exist in neural networks due to the finite switch- ing speed of neurons and amplifiers. Thus, it is important to incorporate time delay in some networks such as delayed cellular neural network, which can be used to solve problems like the processing of moving images. The authors [1–9,11–20] investigated the delayed CGNN _ x i ðtÞ¼a i ðx i ðtÞÞ d i ðx i ðtÞÞ  X n j¼1 b ij g j ðx j ðtÞÞ  X n j¼1 c ij g j ðx j ðt  t ij ÞÞ " # ; i ¼ 1; ... ; n: ð2Þ 0960-0779/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.chaos.2006.04.008 * Corresponding author. E-mail addresses: tingwen.huang@qatar.tamu.edu (T. Huang), licd@cqu.edu.cn (C. Li), gchen@math.tamu.edu (G. Chen). Chaos, Solitons and Fractals 34 (2007) 992–996 www.elsevier.com/locate/chaos