https://doi.org/10.1140/epjp/s13360-023-04060-8
Regular Article
Dynamical detections of a fractional-order neural network with leakage, discrete and distributed delays
1
School of Mathematics and Statistics, Xinyang Normal University, 464000, Xinyang, China
2
School of Mathematics, Southeast University, 210096, Nanjing, China
3
Yonsei Frontier Lab, Yonsei University, 03722, Seoul, South Korea
b huangchengdai@163.com, chdhuang1986@xynu.edu.cn
Received:
13
February
2023
Accepted:
30
April
2023
Published online:
30
June
2023
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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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
