In this paper, we introduce the concept of (ω,c)-asymptotic periodicity within the context of translation-invariant time scales. This concept generalizes various types of function, including asymptotically periodic, asymptotically antiperiodic, asymptotically Bloch periodic, and certain unbounded functions on time scales. We investigate some fundamental properties of this class of functions and apply our findings to cellular neural network (CNN) dynamic equations with leakage and mixed time-varying delays. Using time-scale calculus and a method of contradiction, we establish sufficient conditions for the existence of a unique (ω,c)-asymptotically periodic solution for the considered CNNs and their global exponential stability. These results are completely new across all time domains. In addition, we provide numerical examples and simulations to illustrate the effectiveness of our results for various time scales.
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| http://dx.doi.org/10.1016/j.neunet.2025.107174 | DOI Listing |
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