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2$$^N$$ almost periodic attractors for CNNs with variable and distributed delays. (English) Zbl 1176.34086
Summary: We investigate the dynamics of $$2^N$$ almost periodic attractors for cellular neural networks (CNNs) with variable and distributed delays. By imposing some new assumptions on activation functions and system parameters, we split invariant basin of CNNs into $$2^N$$ compact convex subsets. Then the existence of $$2^N$$ almost periodic solutions lying in compact convex subsets is attained due to employment of the theory of exponential dichotomy and Schauder’s fixed point theorem. Meanwhile, we derive some new criteria for the networks to converge toward these $$2^N$$ almost periodic solutions and exponential attracting domains are also given correspondingly. The obtained results are new and can be applied to a large class of neural networks.

##### MSC:
 34K14 Almost and pseudo-almost periodic solutions to functional-differential equations 92B20 Neural networks for/in biological studies, artificial life and related topics 34K20 Stability theory of functional-differential equations 47N20 Applications of operator theory to differential and integral equations 34K25 Asymptotic theory of functional-differential equations
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