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Dynamical detections of a fractional-order neural network with leakage, discrete and distributed delays

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Abstract

This paper studies the dynamical behaviors of a fractional-order neural network with leakage, discrete and distributed delays. To start with, to conveniently analyze the original system, a four-neuron isovalent system including leakage delay and discrete delay is structured in view of the introduction of virtual neurons. Whereupon we view different delays as bifurcation parameters to go deeply into the stability and bifurcation problems of the developed equivalent systems with different delays. The acquired results indicate that the system will bifurcate and become unstable when the selected delay outstrips the critical value. Furthermore, fractional-order systems converge faster than the counterpart of integer-order systems under the same system parameters, stating clearly that fractional-order systems are capable of delaying the occurrence of bifurcation. Moreover, fractional orders and the decay rate of the influence of past memory have a monumental influence on the bifurcation of the system. Thereby, we can procrastinate or advance the occurrence of the bifurcation via choosing suitable parameters. Lastly, the derived results are neatly verified in terms of numerical experiments.

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No data associated in the manuscript.

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Acknowledgements

The work was jointly supported by the National Natural Science Foundation of China (Nos. 62003290, 12171413), and Program for Innovative Research Team (in Science and Technology) in University of Henan Province (No. 21IRTSTHN014).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xinyang Normal University, Xinyang, 464000, China

    Shuang Liu, Chengdai Huang, Huanan Wang & Yanhui Jing

  2. School of Mathematics, Southeast University, Nanjing, 210096, China

    Jinde Cao

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

    Jinde Cao

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  1. Shuang Liu
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  2. Chengdai Huang
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  3. Huanan Wang
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Correspondence to Chengdai Huang.

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Liu, S., Huang, C., Wang, H. et al. Dynamical detections of a fractional-order neural network with leakage, discrete and distributed delays. Eur. Phys. J. Plus 138, 575 (2023). https://doi.org/10.1140/epjp/s13360-023-04060-8

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