Periodic oscillatory solution in delayed competitive–cooperative neural networks: A decomposition approach

In this paper, the problems of exponential convergence and the exponential stability of the periodic solution for a general class of non-autonomous competitive–cooperative neural networks are analyzed via the decomposition approach. The idea is to divide the connection weights into inhibitory or excitatory types and thereby to embed a competitive–cooperative delayed neural network into an augmented cooperative delay system through a symmetric transformation. Some simple necessary and sufficient conditions are derived to ensure the componentwise exponential convergence and the exponential stability of the periodic solution of the considered neural networks. These results generalize and improve the previous works, and they are easy to check and apply in practice.