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Almost automorphic solutions for neutral type CNNs with time-varying delays and \(D\) operator on time scales. (English) Zbl 1440.34084

Summary: In this paper, we propose a new concept of almost automorphic functions on a new type of almost periodic time scales. Based on inequality analysis techniques on time scales, the exponential dichotomy of linear dynamic equations on time scales and the Banach’s fixed point theorem, we establish the existence and global exponential stability of almost automorphic solutions for a class of neutral type cellular neural networks with time-varying delays and \(D\) operator on time scales. We give a numerical example to illustrate the feasibility of our results.

MSC:

34K40 Neutral functional-differential equations
34K20 Stability theory of functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
34N05 Dynamic equations on time scales or measure chains
47N20 Applications of operator theory to differential and integral equations
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References:

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