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Asymptotic stability of nonlinear fractional delay differential equations with α ∈ (1, 2): An application to fractional delay neural networks.
- Source :
-
Chaos . Apr2024, Vol. 34 Issue 4, p1-13. 13p. - Publication Year :
- 2024
-
Abstract
- We introduce a theorem on linearized asymptotic stability for nonlinear fractional delay differential equations (FDDEs) with a Caputo order α ∈ (1 , 2) , which can be directly used for fractional delay neural networks. It relies on three technical tools: a detailed root analysis for the characteristic equation, estimation for the generalized Mittag-Leffler function, and Lyapunov's first method. We propose coefficient-type criteria to ensure the stability of linear FDDEs through a detailed root analysis for the characteristic equation obtained by the Laplace transform. Further, under the criteria, we provide a wise expression of the generalized Mittag-Leffler functions and prove their polynomial long-time decay rates. Utilizing the well-established Lyapunov's first method, we establish that an equilibrium of a nonlinear Caputo FDDE attains asymptotically stability if its linearization system around the equilibrium solution is asymptotically stable. Finally, as a by-product of our results, we explicitly describe the asymptotic properties of fractional delay neural networks. To illustrate the effectiveness of our theoretical results, numerical simulations are also presented. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10541500
- Volume :
- 34
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Chaos
- Publication Type :
- Academic Journal
- Accession number :
- 177184476
- Full Text :
- https://doi.org/10.1063/5.0188371