Applications of Mathematics, Vol. 67, No. 3, pp. 393-418, 2022
Global exponential stability of pseudo almost automorphic solutions for delayed Cohen-Grosberg neural networks with measure
Chaouki Aouiti, Hediene Jallouli, Mohsen Miraoui
Received July 11, 2020. Published online January 25, 2022.
Abstract: We investigate the Cohen-Grosberg differential equations with mixed delays and time-varying coefficient: Several useful results on the functional space of such functions like completeness and composition theorems are established. By using the fixed-point theorem and some properties of the doubly measure pseudo almost automorphic functions, a set of sufficient criteria are established to ensure the existence, uniqueness and global exponential stability of a $(\mu,\nu)$-pseudo almost automorphic solution. The theory of this work generalizes the classical results on weighted pseudo almost automorphic functions. Finally, a numerical example is provided to illustrate the validity of the proposed theoretical results.
Keywords: pseudo almost automorphic solution; double measure; mixed delays
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Affiliations: Chaouki Aouiti, Hediene Jallouli, University of Carthage, Faculty of Sciences of Bizerta, Department of Mathematics, GAMA Laboratory LR21ES10, BP W, 70 21 Zarzouna, Bizerta, Tunisia, e-mail: chaouki.aouiti@fsb.rnu.tn, jalouli.hedienne@fsb.rnu.tn; Mohsen Miraoui (corresponding author), IPEIK, University of Kairouan, LR11ES53, Kairouan, Tunisia; University of Sfax, Route de l'Aéroport Km 0.5 BP 1169.3029 Sfax, Tunisia, e-mail: miraoui.mohsen@yahoo.fr
