Synchronization analysis of coupled fractional-order neural networks with time-varying delays

In this paper, the complete synchronization and Mittag-Leffler synchronization problems of a kind of coupled fractional-order neural networks with time-varying delays are introduced and studied. First, the sufficient conditions for a controlled system to reach complete synchronization are established by using the Kronecker product technique and Lyapunov direct method under pinning control. Here the pinning controller only needs to control part of the nodes, which can save more resources. To make the system achieve complete synchronization, only the error system is stable. Next, a new adaptive feedback controller is designed, which combines the Razumikhin-type method and Mittag-Leffler stability theory to make the controlled system realize Mittag-Leffler synchronization. The controller has time delays, and the calculation can be simplified by constructing an appropriate auxiliary function. Finally, two numerical examples are given. The simulation process shows that the conditions of the main theorems are not difficult to obtain, and the simulation results confirm the feasibility of the theorems.

Automated summary

This paper introduces and studies the complete synchronization and Mittag-Leffler synchronization problems of a kind of coupled fractional-order neural networks with time-varying delays. Sufficient conditions for complete synchronization of a controlled system are established using the Kronecker product technique and Lyapunov direct method under pinning control. An adaptive feedback controller is designed, which combines the Razumikhin-type method and Mittag-Leffler stability theory to achieve Mittag-Leffler synchronization. Numerical examples are provided to validate the theorems.