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Exponential synchronization of quaternion-valued memristor-based Cohen–Grossberg neural networks with time-varying delays: norm method

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Abstract

In this paper, the exponential synchronization of quaternion-valued memristor-based Cohen–Grossberg neural networks with time-varying delays is discussed. By using the differential inclusion theory and the set-valued map theory, the discontinuous quaternion-valued memristor-based Cohen–Grossberg neural networks are transformed into an uncertain system with interval parameters. A novel controller is designed to achieve the control goal. With some inequality techniques, several criteria of exponential synchronization for quaternion-valued memristor-based Cohen–Grossberg neural networks are given. Different from the existing results using decomposition techniques, a direct analytical approach is used to study the synchronization problem by introducing an improved one-norm method. Moreover, the activation function is less restricted and the Lyapunov analysis process is simpler. Finally, a numerical simulation is given to prove the validity of the main results.

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Funding

Funding were provided by the National Natural Science Foundation of China under Grant 61703354; Key Laboratory of Numerical Simulation of Sichuan Provincial Universities KLNS-2023SZFZ001; Natural Science Foundation of Sichuan Province 2022NSFSC0529; the CUIT (KYQN202324; KYTD202243); the Scientific Research Foundation of Chengdu University of Information Technology KYTZ202184.

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Authors and Affiliations

  1. School of Science, Southwest Petroleum University, Chengdu, 610500, China

    Yanzhao Cheng & Yanchao Shi

  2. College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, 610225, China

    Jun Guo

  3. Key Laboratory of Numerical Simulation of Sichuan Provincial Universities, School of Mathematics and Information Sciences, Neijiang Normal Univeristy, Neijiang, 641000, Sichuan Province, China

    Yanchao Shi

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  1. Yanzhao Cheng
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  2. Yanchao Shi
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  3. Jun Guo
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Correspondence to Yanchao Shi.

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Supported by the National Natural Science Foundation of China under Grant 61703354; Key Laboratory of Numerical Simulation of Sichuan Provincial Universities KLNS-2023SZFZ001; Natural Science Foundation of Sichuan Province 2022NSFSC0529; the Sichuan National Applied Mathematics co-construction project 2022ZX004; the CUIT (KYTD202243); the Scientific Research Foundation of Chengdu University of Information Technology KYTZ202184.

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Cheng, Y., Shi, Y. & Guo, J. Exponential synchronization of quaternion-valued memristor-based Cohen–Grossberg neural networks with time-varying delays: norm method. Cogn Neurodyn (2024). https://doi.org/10.1007/s11571-023-10057-x

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