Lagrange α -Exponential Synchronization of Non-identical Fractional-Order Complex-Valued Neural Networks

Abstract

In this article, Lagrange α-exponential synchronization of non-identical fractional-order complex-valued neural networks (FOCVNNs) is studied. Numerous favorable conditions for achieving Lagrange α-exponential synchronization and α-exponential convergence of the descriptive networks are constructed using additional inequalities and the Lyapunov method. Furthermore, the structure of the α-exponential convergence ball, in which the rate of convergence is linked with the system’s characteristics and order of differential, has also been demonstrated. These findings, which do not require consideration of the existence and uniqueness of equilibrium points, help to generalize and improve previous works and may be used to mono-stable and multi-stable of the FOCVNNs. The salient feature of the article is the graphical exhibition of the effectiveness of the proposed method by using numerical simulation for synchronization of a particular case of the considered fractional-order drive and response systems. © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.