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Zbl 1143.34046
Ren, Fengli; Cao, Jinde
Periodic solutions for a class of higher-order Cohen-Grossberg type neural networks with delays. (English)
[J] Comput. Math. Appl. 54, No. 6, 826-839 (2007). ISSN 0898-1221

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.
[Zhiming Guo (Guangzhou)]

MSC 2000:: *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
34K20 Stability theory of functional-differential equations

Keywords: higher-order Cohen-Grossberg neural network; periodic higher-order Cohen-Grossberg neural network; global attractivity; coincidence degree; Lyapunov functional; $M$-matrix; delay

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