Abstract
In this paper, we study the synchronization of a new fractional-order neural network with multiple delays. Based on the control theory of linear systems with multiple delays, we get the controller to analyse the synchronization of the system. In addition, a suitable Lyapunov function is constructed by using the theory of delay differential inequality, and some criteria ensuring the synchronization of delay fractional neural networks with Caputo derivatives are obtained. Finally, the accuracy of the method is verified by a numerical example.
Highlights
Since Leibniz and L’Hospital first proposed fractional calculus in 1675, people have done a lot of pioneering work in the field [1]. ese research studies involve many fields of science and engineering, such as electromagnetic wave, bioengineering, viscoelastic system, heat conduction, dielectric polarization, and robot [2,3,4,5,6]
We discuss a class of fractional-order neural networks model with multiple time delays which is described by the following differential equation: n
We give some criteria for the globally asymptotic synchronization of the proposed neural networks with multiple delays. e model (7) is taken as the master system, and the following delayed fractional-order differential equation is taken as the slave system: n
Summary
Since Leibniz and L’Hospital first proposed fractional calculus in 1675, people have done a lot of pioneering work in the field [1]. ese research studies involve many fields of science and engineering, such as electromagnetic wave, bioengineering, viscoelastic system, heat conduction, dielectric polarization, and robot [2,3,4,5,6]. Udhayakumar et al [23] considered a fractional-order delayed complex-valued neural networks and afforded some conditions ensuring the projective synchronization of the addressed systems by applying Lyapunov–Krasovskii functional approach and linear matrix inequalities. In 2019, Hu et al [25] discussed a class of time-invariant uncertainty delayed fractional-order neural networks and obtained several global synchronization criteria of the delayed neural networks model by using fractional-order integral Jensen’s inequality and Lyapunov–Krasovskii functions. In 2020, You et al [27] investigated the discrete-time fractional-order delayed complex-valued neural networks and achieved some criteria to ensure the global Mittag-Leffler synchronization for the proposed delayed master-slave systems by devising an effective control scheme and applying Lyapunov’s direct method.
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