Fixed-Time Pinning Common Synchronization and Adaptive Synchronization for Delayed Quaternion-Valued Neural Networks

This article focuses on the fixed-time pinning common synchronization and adaptive synchronization for quaternion-valued neural networks with time-varying delays. First, to reduce transmission burdens and limit convergence time, a pinning controller which only controls partial nodes directly rather than the entire nodes is proposed based on fixed-time control theory. Then, by Lyapunov function approach and some inequalities techniques, fixed-time common synchronization criterion is established. Second, further to realize the self-regulation function of pinning controller, an adaptive pinning controller which can adjust automatically the control gains is developed, the desired fixed-time adaptive synchronization is achieved for the considered system, and the corresponding criterion is also derived. Finally, the availability of these results is tested by simulation example.

Automated summary

This article focuses on fixed-time pinning common synchronization and adaptive synchronization for quaternion-valued neural networks with time-varying delays. By introducing fixed-time control theory and adaptive control gains, the corresponding synchronization criteria are established, and the effectiveness of these results is verified through simulation examples.