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Global exponential stability and periodic solutions of recurrent neural networks with delays. (English) Zbl 0995.92007
Summary: By utilizing the Lyapunov functional method and applying M-matrix and topological degree theory, we analyze the global exponential stability and the existence of periodic solutions of a class of recurrent neural networks with delays. Some simple and new sufficient conditions ensuring existence, uniqueness and global exponential stability of the equilibrium point and periodic solutions of delayed recurrent neural networks are obtained, which do not require the activation functions to be differentiable, bounded and monotone nondecreasing. In addition, two examples are also given to illustrate the theory.
MSC:
92B20General theory of neural networks (mathematical biology)
34K20Stability theory of functional-differential equations
34K13Periodic solutions of functional differential equations