Iranian Journal of Numerical Analysis and Optimization

Iranian Journal of Numerical Analysis and Optimization

Synchronization and control of discrete incommensurate fractional-order and variable-order neural networks

Document Type : Research Article

Authors
1 Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan.
2 Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE.
3 Department of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, Jordan.
4 Laboratory of Dynamical Systems and Control, University of Oum EL-Bouaghi, Oum El Bouaghi 04000, Algeria.
5 Department of Mathematics and Computer Science, University of Oum EL-Bouaghi, Oum El Bouaghi 04000, Algeria.
Abstract
The examination of dynamics and synchronization within discrete fractional neural networks has attracted notable interest in contemporary studies. Nevertheless, current research has primarily focused on commensurate discrete fractional-order neural networks. This study aims to explore the synchronization of incommensurate discrete fractional neural networks, spanning both constant and variable orders. By employing linear feedback control techniques, we establish a satisfactory criterion to guarantee the synchronization of noncommensurate discrete fractional neural networks with constant orders. This condition is formulated in terms of linear matrix inequalities, offering a systematic approach to synchronization. Furthermore, under specific conditions, the Lyapunov functional is employed to analyze the synchronization of non-commensurate discrete fractional neural networks with variable orders. This synchronization condition is solely dependent on the system parameters, facilitating easy verification and implementation. In order to confirm the efficacy and practicality of the proposed methodologies, two numerical examples are selected and presented, demonstrating the successful synchronization of incommensurate discrete fractional neural networks.
Keywords
Subjects

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