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Bifurcation−Driven Tipping in A Novel Bicyclic Crossed Neural Network with Multiple Time Delays

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Abstract

Anatomical experiments have proved that a large number of ring structures exist in neural networks. Therefore, many scholars have focused on modeling and dynamic analysis of multi-ring neural networks. However, most current research regarding multi-ring neural networks considers the case that rings share only one neuron with each other. This type of connection among rings fails to adequately capture the complex structure of actual neural networks. In this paper, we consider two sharing neurons between rings and propose a bicyclic crossed neural network model with multiple time delays. Then, the stability condition of the proposed neural network model is given without time delays. By choosing the sum of time delays as the bifurcation parameter, the occurrence conditions of tipping due to Hopf bifurcation are derived, and the tipping point (bifurcation threshold) is accurately determined. In addition, the explicit formulae for ascertaining the Hopf bifurcation properties are given by utilizing the center manifold theory, which further reveals the evolutionary tipping mechanism. Finally, through numerical simulations, the validity of the theoretical analysis is verified. The results show that with the increase in time delays, the network will gradually lose stability, and the tipping driven by Hopf bifurcation will occur. Moreover, the magnitude of time delays emerges as a significant determinant of both the amplitude and the oscillation period of unstable neurons.

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Data Availability

The data that support the findings of this study are available from the corresponding author, [MX], upon reasonable request.

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Acknowledgements

This work is supported in part by the National Natural Science Foundation of China under Grant 62073172 and the Natural Science Foundation of Jiangsu Province of China under Grant BK20221329.

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Authors and Affiliations

  1. College of Automation and College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing, 210023, China

    Xiangyu Du, Min Xiao, Jie Ding & Jiajin He

  2. School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China

    Yi Yao

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

    Jinde Cao

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

    Jinde Cao

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  1. Xiangyu Du
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  2. Min Xiao
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  3. Jie Ding
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  4. Jiajin He
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Correspondence to Min Xiao.

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Du, X., Xiao, M., Ding, J. et al. Bifurcation−Driven Tipping in A Novel Bicyclic Crossed Neural Network with Multiple Time Delays. Cogn Comput 16, 278–292 (2024). https://doi.org/10.1007/s12559-023-10199-4

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