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Periodic solutions for a class of higher-order Cohen-Grossberg type neural networks with delays. (English) Zbl 1143.34046
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.
##### MSC:
 34K13 Periodic solutions of functional differential equations 34K25 Asymptotic theory of functional-differential equations 37N25 Dynamical systems in biology 92B20 General theory of neural networks (mathematical biology) 34K20 Stability theory of functional-differential equations