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Finite Time Anti-synchronization of Quaternion-Valued Neural Networks with Asynchronous Time-Varying Delays

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Abstract

In this paper, we consider the finite time anti-synchronization (A-SYN) of master-slave coupled quaternion-valued neural networks, where the time-varying delays can be asynchronous and unbounded. Without adopting the general decomposition method, the quaternion-valued state is considered as a whole, which greatly reduces the hassle of further analysis and calculations. The designed controller is delay-free, and the terms with time delay do not need to be bounded globally. Several sufficient conditions for ensuring the finite time A-SYN are obtained under 1-norm and 2-norm respectively. The A-SYN error will be proved to evolve from the initial value to 1 in finite time, and evolve from 1 to 0 also in finite time, hence the finite time A-SYN is proved, which is called two-phases-method. Moreover, adaptive rules for control strengths are also designed to realize the finite time A-SYN. Lastly, a numerical example is presented to demonstrate the correctness and effectiveness of our obtained results.

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Acknowledgements

This work was supported by the National Science Foundation of China under Grant Nos. 61673298, 61203149; Shanghai Rising-Star Program of China under Grant No. 17QA1404500; Natural Science Foundation of Shanghai under Grant No. 17ZR1445700; the Fundamental Research Funds for the Central Universities of Tongji University.

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Authors and Affiliations

  1. Department of Computer Science and Technology, Tongji University, Shanghai, 201804, China

    Zihan Li & Xiwei Liu

  2. Key Laboratory of Embedded System and Service Computing (Tongji University), Ministry of Education, Shanghai, 201804, China

    Xiwei Liu

  3. Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai, 200433, China

    Xiwei Liu

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  1. Zihan Li
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  2. Xiwei Liu
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Correspondence to Xiwei Liu.

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Li, Z., Liu, X. Finite Time Anti-synchronization of Quaternion-Valued Neural Networks with Asynchronous Time-Varying Delays. Neural Process Lett 52, 2253–2274 (2020). https://doi.org/10.1007/s11063-020-10348-y

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