Exponential stability for impulsive Cohen‐Grossberg neural networks with time‐varying delays and distributed delays
Cheng‐De Zheng, Ri‐Ming Sun, Zhanshan Wang · International Journal of Intelligent Computing and Cybernetics · 2013
Purpose The purpose of this paper is to develop a methodology for the existence and global exponential stability of the unique equilibrium point of a class of impulsive Cohen‐Grossberg neural networks. Design/methodology/approach The authors perform M‐matrix theory and homeomorphism mapping principle to investigate a class of impulsive Cohen‐Grossberg networks with time‐varying delays and distributed delays. The approach builds on new sufficient criterion without strict conditions imposed on self‐regulation functions. Findings The authors' approach results in new sufficient criteria easy to verify but without the usual assumption that the activation functions are bounded and the time‐varying delays are differentiable. An example shows the effectiveness and superiority of the obtained results over some previously known results. Originality/value The novelty of the proposed approach lies in removing the usual assumption that the activation functions are bounded and the time‐varying delays are differentiable, and the use of M‐matrix theory and homeomorphism mapping principle for the existence and global exponential stability of the unique equilibrium point of a class of impulsive Cohen‐Grossberg neural networks.