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Detections of bifurcation in a fractional-order Cohen-Grossberg neural network with multiple delays

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Abstract

The dynamics of integer-order Cohen-Grossberg neural networks with time delays has lately drawn tremendous attention. It reveals that fractional calculus plays a crucial role on influencing the dynamical behaviors of neural networks (NNs). This paper deals with the problem of the stability and bifurcation of fractional-order Cohen-Grossberg neural networks (FOCGNNs) with two different leakage delay and communication delay. The bifurcation results with regard to leakage delay are firstly gained. Then, communication delay is viewed as a bifurcation parameter to detect the critical values of bifurcations for the addressed FOCGNN, and the communication delay induced-bifurcation conditions are procured. We further discover that fractional orders can enlarge (reduce) stability regions of the addressed FOCGNN. Furthermore, we discover that, for the same system parameters, the convergence time to the equilibrium point of FONN is shorter (longer) than that of integer-order NNs. In this paper, the present methodology to handle the characteristic equation with triple transcendental terms in delayed FOCGNNs is concise, neoteric and flexible in contrast with the prior mechanisms owing to skillfully keeping away from the intricate classified discussions. Eventually, the developed analytic results are nicely showcased by the simulation examples.

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Acknowledgements

This work was jointly supported by the Youth Research Fund Project of Xinyang Normal University under Grant No.2022-QN-044 and the Nanhu Scholars Program for Young Scholars of Xinyang Normal University and Graduate Research and Innovation Fund Project of Xinyang Normal University under Grant No.2021KYJJ47.

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Authors and Affiliations

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

    Chengdai Huang & Shansong Mo

  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. Chengdai Huang
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  2. Shansong Mo
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  3. Jinde Cao
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Correspondence to Chengdai Huang.

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Huang, C., Mo, S. & Cao, J. Detections of bifurcation in a fractional-order Cohen-Grossberg neural network with multiple delays. Cogn Neurodyn 18, 1379–1396 (2024). https://doi.org/10.1007/s11571-023-09934-2

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