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

Biwen Li; Xuan Cheng; Biwen Li; Xuan Cheng

doi:10.3934/mbe.2023665

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 8: 14846-14865. doi: 10.3934/mbe.2023665

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Research article

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

Biwen Li ,
Xuan Cheng ^,

School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China

Received: 07 April 2023 Revised: 13 June 2023 Accepted: 28 June 2023 Published: 10 July 2023

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.
- coupled neural networks,
- fractional order,
- complete synchronization,
- Mittag-Leffler synchronization,
- time-varying delays
Citation: Biwen Li, Xuan Cheng. Synchronization analysis of coupled fractional-order neural networks with time-varying delays[J]. Mathematical Biosciences and Engineering, 2023, 20(8): 14846-14865. doi: 10.3934/mbe.2023665

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Abstract

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.

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