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Novel algebraic criteria on global Mittag–Leffler synchronization for FOINNs with the Caputo derivative and delay

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Abstract

This paper focuses on the global Mittag–Leffler (M–L) synchronization for fractional-order inertial neural networks (FOINNs) including the Caputo derivative and delay. By choosing an appropriate variable transformation, the considered system including the inertial term is transformed into two fractional-order nonlinearly coupled interconnected subsystems. Combining with the delayed-feedback controller, fractional Lyapunov functional approach and inequality analysis technique, multi sets of novel algebraic criteria on the global M–L synchronization between derive-response systems are established. The main prominent highlight of this paper is that the proposed results are characterized by the algebraic inequalities form, which can simplify the calculation and facilitate the test. Two numerical simulation examples validate the theoretical results.

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Acknowledgements

This work was supported the Natural Science Foundation of Anhui Province of China (No. 1908085MA01), the Natural Science Foundation of the Higher Education Institutions of Anhui Province (Nos. KJ2019A0557, KJ2019A0573) and the Top Young Talents Program of Higher Learning Institutions of Anhui Province (No. gxyq2019048).

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  1. School of Mathematics and Physics, Anqing Normal University, Anqing, 246133, People’s Republic of China

    Yuhong Cheng, Hai Zhang, Weiwei Zhang & Hongmei Zhang

  2. College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, People’s Republic of China

    Weiwei Zhang

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  1. Yuhong Cheng
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Correspondence to Hai Zhang.

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Cheng, Y., Zhang, H., Zhang, W. et al. Novel algebraic criteria on global Mittag–Leffler synchronization for FOINNs with the Caputo derivative and delay. J. Appl. Math. Comput. 68, 3527–3544 (2022). https://doi.org/10.1007/s12190-021-01672-0

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