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Exponential periodic attractor of impulsive BAM networks with finite distributed delays. (English) Zbl 1197.34124

Summary: We investigate a class of impulsive bidirectional associative memory (BAM) networks with both periodic coefficients and finite distributed delays. New criteria are established for the existence of an exponential periodic attractor, which generalize and improve the previously known results. Our criteria are less restrictive and can be applied to impulsive or non-impulsive BAM networks with a broad range of activation functions without differentiability and strict monotonicity. Moreover, our results are given in terms of system parameters and finite delay kernels of impulsive BAM networks by employing inequality technique, $M$-matrix and spectral theory. Finally, an example is given to show the feasibility and effectiveness of our results.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

##### MSC:
 34K13 Periodic solutions of functional differential equations 34K20 Stability theory of functional-differential equations 34K45 Functional-differential equations with impulses 37N25 Dynamical systems in biology 92B20 General theory of neural networks (mathematical biology)