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Hopf Bifurcation Analysis of a Delayed Fractional BAM Neural Network Model with Incommensurate Orders

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Abstract

In this paper, a six-neuron incommensurate fractional order BAM neural network model with multi-delays is considered. We demonstrate that the equilibrium point of the system loses its stability and Hopf bifurcation emerges when the delay passes through a critical value. And the relationship between the critical delay of Hopf bifurcation and size of fractional orders is found. Finally, some numerical simulations are given to verify the validity of the theoretical results.

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Authors and Affiliations

  1. School of Mathematics and Physics, University of South China, Hengyang, 421001, Hunan, People’s Republic of China

    Bingbing Li, Maoxin Liao & Weinan Li

  2. Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang, 550004, Guizhou, People’s Republic of China

    Changjin Xu

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  1. Bingbing Li
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  2. Maoxin Liao
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  3. Changjin Xu
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  4. Weinan Li
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Correspondence to Maoxin Liao.

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Supported partly by the National Natural Science Foundation of China (12261015, 61673008), Joint Fund Project of Guizhou University of Finance and Economics and Institute of International Trade and Economic Cooperation of Ministry of Commerce on Contiguous areas of extreme poverty Poor peasant psychological Poverty alleviation(2017SWBZD09), Hunan Natural Science Foundation (2020JJ4516), Hunan Provincial Key Foundation of Education Department (17A181), Hunan Key Laboratory of Mathematical Modeling and Scientific Computing.

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Li, B., Liao, M., Xu, C. et al. Hopf Bifurcation Analysis of a Delayed Fractional BAM Neural Network Model with Incommensurate Orders. Neural Process Lett 55, 5905–5921 (2023). https://doi.org/10.1007/s11063-022-11118-8

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