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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.
34K13Periodic solutions of functional differential equations
34K25Asymptotic theory of functional-differential equations
37N25Dynamical systems in biology
92B20General theory of neural networks (mathematical biology)
34K20Stability theory of functional-differential equations