Fixed/Preassigned-Time Synchronization of Fully Quaternion-Valued Cohen–Grossberg Neural Networks with Generalized Time Delay

Shichao Jia, Cheng Hu and Haijun Jiang ()
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Shichao Jia: College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China
Cheng Hu: College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China
Haijun Jiang: College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China

Mathematics, 2023, vol. 11, issue 23, 1-20

Abstract: This article is concerned with fixed-time synchronization and preassigned-time synchronization of Cohen–Grossberg quaternion-valued neural networks with discontinuous activation functions and generalized time-varying delays. Firstly, a dynamic model of Cohen–Grossberg neural networks is introduced in the quaternion field, where the time delay successfully integrates discrete-time delay and proportional delay. Secondly, two types of discontinuous controllers employing the quaternion-valued signum function are designed. Without utilizing the conventional separation technique, by developing a direct analytical approach and using the theory of non-smooth analysis, several adequate criteria are derived to achieve fixed-time synchronization of Cohen–Grossberg neural networks and some more precise convergence times are estimated. To cater to practical requirements, preassigned-time synchronization is also addressed, which shows that the drive-slave networks reach synchronization within a specified time. Finally, two numerical simulations are presented to validate the effectiveness of the designed controllers and criteria.

Keywords: Cohen–Grossberg quaternion-valued neural network; fixed-time synchronization; preassigned-time synchronization; non-separation approach (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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