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Impulsive Hopfield-type neural network system with piecewise constant argument. (English) Zbl 1202.92001
Authors’ abstract: We introduce an impulsive Hopfield-type neural network system with piecewise constant argument of generalized type. Sufficient conditions for the existence of the unique equilibrium are obtained. Existence and uniqueness of solutions of such systems are established. Stability criterion based on linear approximation is proposed. Some sufficient conditions for the existence and stability of periodic solutions are derived. An example with numerical simulations is given to illustrate our results.
MSC:
92B20General theory of neural networks (mathematical biology)
34A37Differential equations with impulses
68T05Learning and adaptive systems