Asymptotical stability and synchronization of Riemann–Liouville fractional delayed neural networks

In this paper, we investigate the asymptotical stability and synchronization of fractional neural networks. Multiple time-varying delays and distributed delays are taken into consideration simultaneously. First, by applying the Banach’s fixed point theorem, the existence and uniqueness of fractional...

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Bibliographic Details
Published in:Computational & applied mathematics 2023-02, Vol.42 (1), Article 20
Main Authors: Zhang, Yufeng, Li, Jing, Zhu, Shaotao, Wang, Hongwu
Format: Article
Language:English
Subjects:
Adaptive control
Applications of Mathematics
Applied physics
Asymptotic properties
Computational mathematics
Computational Mathematics and Numerical Analysis
Existence theorems
Fixed points (mathematics)
Liapunov direct method
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Neural networks
Stability
Synchronism
Uniqueness theorems
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Summary:In this paper, we investigate the asymptotical stability and synchronization of fractional neural networks. Multiple time-varying delays and distributed delays are taken into consideration simultaneously. First, by applying the Banach’s fixed point theorem, the existence and uniqueness of fractional delayed neural networks are proposed. Then, to guarantee the asymptotical stability of the demonstrated system, two sufficient conditions are derived by integral-order Lyapunov direct method. Furthermore, two synchronization criteria are presented based on the adaptive controller. The above results significantly generalize the existed conclusions in the previous works. At last, numerical simulations are taken to check the validity and feasibility of the achieved methods.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-022-02122-8