Projective synchronization for quaternion-valued memristor-based neural networks under time-varying delays

1.
College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, China
2.
Key Laboratory of Numerical Simulation of Sichuan Provincial Universities, School of Mathematics and Information Sciences, Neijiang Normal University, Neijiang 641000, China
3.
School of Science, Southwest Petroleum University, Chengdu 610500, China
4.
School of Mathematics and Physics, Hunan University of Arts and Science, Changde 415000, China

Received: 20 August 2024Revised: 08 October 2024Accepted: 12 October 2024Published: 17 October 2024

In this paper, the projective synchronization of quaternion-valued memristor-based neural networks with time-varing delays was studied. First, by utilizing set-valued map and differential inclusion theories, we reformulated the networks as an uncertain system with interval parameters. Then, through designing a novel controller and utilizing Lyapunov function and Young's inequality, several new synchronization conditions for projection synchronization of quaternion-valued memristor-based neural networks were obtained. Finally, the effectiveness of this method was demonstrated through a numerical example, underscoring its practical applicability.
- projective synchronization,
- quaternion-valued,
- time-varying delays,
- memristor-based neural networks
Citation: Jun Guo, Yanchao Shi, Yanzhao Cheng, Weihua Luo. Projective synchronization for quaternion-valued memristor-based neural networks under time-varying delays[J]. Networks and Heterogeneous Media, 2024, 19(3): 1156-1181. doi: 10.3934/nhm.2024051
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Abstract

In this paper, the projective synchronization of quaternion-valued memristor-based neural networks with time-varing delays was studied. First, by utilizing set-valued map and differential inclusion theories, we reformulated the networks as an uncertain system with interval parameters. Then, through designing a novel controller and utilizing Lyapunov function and Young's inequality, several new synchronization conditions for projection synchronization of quaternion-valued memristor-based neural networks were obtained. Finally, the effectiveness of this method was demonstrated through a numerical example, underscoring its practical applicability.

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