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On the existence and stability of the periodic solution in the Cohen-Grossberg neural network with time delay and high-order terms. (English) Zbl 1104.34051
A class of Cohen-Grossberg neural networks with delay and higher-order terms is studied. Existence of periodic solutions is proved by use of the Gain’s and Mawhin’s continuation theorem. Sufficient conditions for global exponential and asymptotical stability of the periodic solutions are derived by the authors by means of a Lyapunov functional and linear matrix inequality. Numerical simulations of two examples are given as well.

MSC:
34K13 Periodic solutions to functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
34K20 Stability theory of functional-differential equations
34K60 Qualitative investigation and simulation of models involving functional-differential equations
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