Global asymptotic stability of a class of generalized BAM neural networks with reaction-diffusion terms and mixed time delays

Abstract

Abstract In this paper, a novel linear matrix inequality (LMI)-based sufficient condition, which guarantees the existence and global asymptotic stability of a class of generalized bidirectional associative memory (BAM) neural networks with reaction-diffusion terms and mixed time delays, is obtained by using inequality technique, degree theory, LMI method and constructing Lyapunov functional. The mixed time delays consist of both the discrete delays and the infinitely distributed delays. The results generalize and improve the earlier publications under the assumption that the activation functions only satisfy general global Lipschitz conditions. Two simple examples are provided to demonstrate the effectiveness of the proposed theoretical results. These results can be applied to design globally asymptotically stable networks and thus have important significance in both theory and applications.