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The Exponential Synchronization and Asymptotic Synchronization of Quaternion-Valued Memristor-Based Cohen–Grossberg Neural Networks with Time-Varying Delays

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Abstract

In this paper, the exponential synchronization and global asymptotic synchronization of quaternion-valued memristor-based Cohen–Grossberg neural networks with time-varying delays are discussed. Firstly, by using the differential inclusion theory and the set-valued map theory, the discontinuous quaternion-valued memristor-based Cohen–Grossberg neural networks is transformed into an uncertain system with interval parameters. Different from the existing results, this paper deals with the Cohen–Grossberg neural network based on the quaternary value memristor directly, which simplifies the proof process. Secondly, two suitable controllers are designed to achieve the control objective. Then, with some inequality techniques, criteria of global exponential synchronization and global asymptotic synchronization for quaternion-valued memristor-based Cohen–Grossberg neural networks are given. Finally, two numerical simulations are given to prove the validity of the main results.

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Funding

Supported by the National Natural Science Foundation of China under Grant 61703354; Natural Science Foundation of Sichuan Province 2022NSFSC0529; Youth Science and Technology Innovation Team of Southwest Petroleum University for Artificial intelligence network 2019CXTD08.

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

    Yanzhao Cheng & Yanchao Shi

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  1. Yanzhao Cheng
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  2. Yanchao Shi
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All of the authors agree to the submission of this paper. The dataries generated during the current study are available from the corresponding author on reasonable request. YC and YS wrote the main manuscript text. All authors reviewed the manuscript.

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Correspondence to Yanchao Shi.

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Supported by the National Natural Science Foundation of China under Grant 61703354; Natural Science Foundation of Sichuan Province 2022NSFSC0529; Youth Science and Technology Innovation Team of Southwest Petroleum University for Artificial intelligence network 2019CXTD08.

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Cheng, Y., Shi, Y. The Exponential Synchronization and Asymptotic Synchronization of Quaternion-Valued Memristor-Based Cohen–Grossberg Neural Networks with Time-Varying Delays. Neural Process Lett 55, 6637–6656 (2023). https://doi.org/10.1007/s11063-023-11152-0

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