Global stability and synchronization of stochastic discrete-time variable-order fractional-order delayed quaternion-valued neural networks

Jie Ran, Yonghui Zhou and Hao Pu

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 226, issue C, 413-437

Abstract: This study proposes a novel tool for neural network modeling by integrating quaternion theory, discrete fractional calculus, and stochastic analysis, thereby introducing a stochastic discrete fractional delayed quaternion-valued neural network model. Firstly, we prove the existence and uniqueness of the equilibrium point for the model by using the homeomorphism mapping theory. Secondly, we give some new inequalities in the quaternion domain. Through these inequalities and Lyapunov theory, we establish sufficient linear matrix inequality (LMI) conditions on the global mean square stability and global mean square Mittag-Leffler stability for the model. Furthermore, the linear feedback control approach is employed to derive sufficient LMI conditions that achieve the model’s global mean square synchronization and global mean square Mittag-Leffler synchronization. Finally, several numerical examples validate the findings obtained.

Keywords: Discrete fractional calculus; Stochastic stability; Synchronization; Time delay; Quaternion-valued neural networks (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:226:y:2024:i:c:p:413-437

DOI: 10.1016/j.matcom.2024.07.017

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