Exponential projective synchronization analysis for quaternion-valued memristor-based neural networks with time delays

Jun Guo; Yanchao Shi; Weihua Luo; Yanzhao Cheng; Shengye Wang; Jun Guo; Yanchao Shi; Weihua Luo; Yanzhao Cheng; Shengye Wang

doi:10.3934/era.2023285

Electronic Research Archive

2023, Volume 31, Issue 9: 5609-5631. doi: 10.3934/era.2023285

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Exponential projective synchronization analysis for quaternion-valued memristor-based neural networks with time delays

1.
College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, China
2.
School of Science, Southwest Petroleum University, Chengdu 610500, China
3.
School of Mathematics and Physics, Hunan University of Arts and Science, Changde, Hunan 415000, China

Received: 04 June 2023 Revised: 07 July 2023 Accepted: 24 July 2023 Published: 15 August 2023

The issues of exponential projective synchronization and adaptive exponential projective synchronization are analyzed for quaternion-valued memristor-based neural networks (QVMNNs) with time delays. Different from the results of existing decomposition techniques, a direct analytical approach is used to discuss the projection synchronization problem. First, in the framework of measurable selection and differential inclusion, the QVMNNs is transformed into a system with parametric uncertainty. Next, the sign function related to quaternion is introduced. Different proper control schemes are designed and several criteria for ascertaining exponential projective synchronization and adaptive exponential projective synchronization are derived based on Lyapunov theory and the properties of sign function. Furthermore, several corollaries about global projective synchronization are proposed. Finally, the reliability and validity of our results are substantiated by two numerical examples and its corresponding simulation.
Citation: Jun Guo, Yanchao Shi, Weihua Luo, Yanzhao Cheng, Shengye Wang. Exponential projective synchronization analysis for quaternion-valued memristor-based neural networks with time delays[J]. Electronic Research Archive, 2023, 31(9): 5609-5631. doi: 10.3934/era.2023285

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Abstract

The issues of exponential projective synchronization and adaptive exponential projective synchronization are analyzed for quaternion-valued memristor-based neural networks (QVMNNs) with time delays. Different from the results of existing decomposition techniques, a direct analytical approach is used to discuss the projection synchronization problem. First, in the framework of measurable selection and differential inclusion, the QVMNNs is transformed into a system with parametric uncertainty. Next, the sign function related to quaternion is introduced. Different proper control schemes are designed and several criteria for ascertaining exponential projective synchronization and adaptive exponential projective synchronization are derived based on Lyapunov theory and the properties of sign function. Furthermore, several corollaries about global projective synchronization are proposed. Finally, the reliability and validity of our results are substantiated by two numerical examples and its corresponding simulation.

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