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Synchronization of Quaternion Valued Neural Networks with Mixed Time Delays Using Lyapunov Function Method

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Abstract

This article is concerned with the fixed time synchronization for a class of Quaternion valued neural networks (QVNNs) with mixed time varying delays. Firstly, the QVNNs are separated into four equivalent real valued neural networks (RVNNs). Then, a novel suitable controller is designed to establish the fixed time synchronization of the QVNNs with the help of Lyapunov function. To give a glimpse, the finite time and fixed time stability definitions are proposed. Two different expressions of settling time are obtained by using two different lemmas. Finally, the validation of the theoretical results is shown through numerical simulation to a specific example.

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Acknowledgements

The third author acknowledges the project Grant provided by the SERB, Government of India under the MATRICS scheme (File No.: MTR/2020/000053). The Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, Saudi Arabia has funded this project, under grant no. (FP-114-43).

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Authors and Affiliations

  1. Department of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University), Varanasi, 221005, India

    Sunny Singh, Umesh Kumar & Subir Das

  2. Department of Information Technology, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, Saudi Arabia

    F. Alsaadi

  3. School of Mathematics, Southeast University, Nanjing, 211189, People’s Republic of China

    Jinde Cao

  4. Yonsei Frontier Lab, Yonsei University, Seoul, 03722, South Korea

    Jinde Cao

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  1. Sunny Singh
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  2. Umesh Kumar
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  3. Subir Das
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  4. F. Alsaadi
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Correspondence to Jinde Cao.

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Singh, S., Kumar, U., Das, S. et al. Synchronization of Quaternion Valued Neural Networks with Mixed Time Delays Using Lyapunov Function Method. Neural Process Lett 54, 785–801 (2022). https://doi.org/10.1007/s11063-021-10657-w

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