Eur. Phys. J. Spec. Top. (2022) 231: 1815-1829
https://doi.org/10.1140/epjs/s11734-022-00442-8

Regular Article

Chaotic fractional discrete neural networks based on the Caputo h-difference operator: stabilization and linear control laws for synchronization

¹ Department of Mathematics, University of Larbi Tebessi, 12002, Tebessa, Algeria
² Department of Mathematics and Computer science, University of Larbi Ben M’hidi, Oum El Bouaghi, Algeria
³ Laboratory of Dynamical Systems and Control, University of Larbi Ben M’hidi, Oum El Bouaghi, Algeria
⁴ Dipartimento Ingegneria Innovazione, Universita del Salento, 73100, Lecce, Italy
⁵ Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

^f phamvietthanh@tdtu.edu.vn

Received: 7 February 2021
Accepted: 10 January 2022
Published online: 29 January 2022

Abstract

Chaotic dynamics and synchronization in fractional systems described by non-integer order difference operators have attracted increasing attention in recent years. However, very few papers have been published regarding the chaotic behaviors of fractional discrete-time neural networks and their synchronization properties. A novel chaotic h-fractional discrete neural network model is presented in this paper. This model is described using the h-fractional Caputo difference operator of order . The paper also presents a novel theorem, which assures that two chaotic fractional discrete neural networks achieve synchronized dynamics using very simple linear control laws. Additionally, the chaotic dynamics of the network are stabilized at the origin via a suitable controller. Finally, simulation results are carried out to demonstrate the feasibility of the theoretical results developed herein.