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Dynamics of a class of Cohen–Grossberg neural networks with time-varying delays. (English) Zbl 1123.34053
This paper considers a class of Cohen-Grossberg neural networks with time-varying delays. By means of Brouwer’s fixed point theorem, matrix theory, a continuation theorem of the coincidence degree and inequality analysis, without assuming the boundedness, monotonicity, and differentiability of activation functions and any symmetry of interconnections, the author establishes some sufficient conditions for the global exponential stability of a unique equilibrium and the existence of periodic solution for the Cohen-Grossberg neural network with time-varying delays. The results are all independent of the delays and may be more convenient to design a circuit network. Using numerical simulation, the author gives two examples to demonstrate the results.
MSC:
34K13Periodic solutions of functional differential equations
34K20Stability theory of functional-differential equations
92B20General theory of neural networks (mathematical biology)