Dynamics of a multiplex neural network with delayed couplings

Abstract

Multiplex networks have drawn much attention since they have been observed in many systems, e.g., brain, transport, and social relationships. In this paper, the nonlinear dynamics of a multiplex network with three neural groups and delayed interactions is studied. The stability and bifurcation of the network equilibrium are discussed, and interesting neural activities of the network are explored. Based on the neuron circuit, transfer function circuit, and time delay circuit, a circuit platform of the network is constructed. It is shown that delayed couplings play crucial roles in the network dynamics, e.g., the enhancement and suppression of the stability, the patterns of the synchronization between networks, and the generation of complicated attractors and multi-stability coexistence.

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Acknowledgements

The authors thank the anonymous reviewers for their helpful comments and suggestions that have helped to improve the presentation.

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Correspondence to Xiaochen Mao.

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Project supported by the National Natural Science Foundation of China (Nos. 11872169 and 11472097), the Fundamental Research Funds for the Central Universities of China (No. B200202114), and the Natural Science Foundation of Jiangsu Province of China (No. BK20191295)

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Cite this article

Mao, X., Li, X., Ding, W. et al. Dynamics of a multiplex neural network with delayed couplings. Appl. Math. Mech.-Engl. Ed. (2021). https://doi.org/10.1007/s10483-021-2709-6

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Key words

  • neural network
  • time delay
  • synchronization
  • coexisting attractor

Chinese Library Classification

  • O241

2010 Mathematics Subject Classification

  • 65D15