Periodic solutions for a class of higher-order Cohen-Grossberg type neural networks with delays (Q2469932)

This paper deals with the existence and global attractivity of periodic solutions to a class of higher-order Cohen-Grossberg type neural networks with delays. Sufficient conditions are obtained to ascertain existence and global attractivity of a periodic solution without the constraints of symmetry of the connection matrix, monotonicity, and smoothness of the activation function. The proposed model is a generalization of the classical Cohen-Grossberg model, as well as Hopfield neural networks. The proofs are based on Gains and Mawhin's continuation theorem of coincidence degree, a Lyapunov functional and a nonsingular \(M\)-matrix. An example is also given to illustrate the effectiveness of the proposed criteria.