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Existence and globally exponential stability of equilibrium for BAM neural networks with impulses. (English) Zbl 1144.34347
Summary: A class of two-layer heteroassociative networks called bidirectional associative memory (BAM) networks with impulses is studied. Some new sufficient conditions are established for the existence and globally exponential stability of a unique equilibrium, which generalize and improve the previously known results. The sufficient conditions are easy to verify and when the impulsive jumps are absent the results reduce to those of the nonimpulsive systems. The approaches are based on employing Banach’s fixed point theorem, matrix theory and its spectral theory. Our results generalize and significantly improve the previous known results due to this method. Examples are given to show the feasibility and effectiveness of our results.
34D23Global stability of ODE
34D20Stability of ODE
34A37Differential equations with impulses
92B20General theory of neural networks (mathematical biology)