A decomposition approach to analysis of competitive-cooperative neural networks with delay

Competitive-cooperative or inhibitory-excitatory configurations abound in neural networks. It is demonstrated here how such a configuration may be exploited to give a detailed characterization of the fixed point dynamics in general neural networks with time delay. The idea is to divide the connection weights into inhibitory and excitatory types and thereby to embed a competitive-cooperative delay neural network into an augmented cooperative delay system through a symmetric transformation. This allows for the use of the powerful monotone properties of cooperative systems. By the method, we derive several simple necessary and sufficient conditions on guaranteed trapping regions and guaranteed componentwise (exponential) convergence of the neural networks. The results relate specific decay rate and trajectory bounds to system parameters and are therefore of practical significance in designing a network with desired performance. (C) 2003 Elsevier Science B.V. All rights reserved.