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

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.

Automated summary

This article investigates fixed-time synchronization and preassigned-time synchronization of Cohen-Grossberg quaternion-valued neural networks with discontinuous activation functions and generalized time-varying delays. It introduces a dynamic model in the quaternion field and designs two types of discontinuous controllers utilizing the quaternion-valued signum function. By developing a direct analytical approach and using the theory of non-smooth analysis, it derives several criteria for achieving fixed-time synchronization and estimates more precise convergence times. The article also addresses preassigned-time synchronization for practical requirements.