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Global adaptive matrix-projective synchronization of delayed fractional-order competitive neural network with different time scales

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Abstract

In this paper, by using the adaptive control method, the global matrix-projective synchronization of delayed fractional-order competitive neural network with different time scales is researched for the first time. Firstly, the fractional-order global matrix-projective synchronization is defined. Then, in order to achieve the matrix-projective synchronization, the sufficient condition is obtained under an adaptive controller and its effectiveness is proved by combining the fractional-order Barbalat theory with a suitable Lyapunov–Krasovskii functional as well as some fractional-order differential inequalities. And all unknown parameters are identified and estimated to the fixed constants successfully. Finally, as applications, a numerical example with simulations is employed to demonstrate the feasibility and efficiency of the new synchronization analysis.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (11872201, 11572148 and 11632008).

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Authors and Affiliations

  1. Department of Mechanics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People’s Republic of China

    Jinman He

  2. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People’s Republic of China

    Fangqi Chen

  3. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, People’s Republic of China

    Fangqi Chen

  4. School of Mechanical and Electrical Engineering, Qilu Institute of Technology, Jinan, People’s Republic of China

    Tengfei Lei

  5. Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang, 212013, People’s Republic of China

    Qinsheng Bi

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  1. Jinman He
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Correspondence to Jinman He.

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He, J., Chen, F., Lei, T. et al. Global adaptive matrix-projective synchronization of delayed fractional-order competitive neural network with different time scales. Neural Comput & Applic 32, 12813–12826 (2020). https://doi.org/10.1007/s00521-020-04728-7

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  • DOI: https://doi.org/10.1007/s00521-020-04728-7

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