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Spatiotemporal dynamics on a class of (n+1)-dimensional reaction–diffusion neural networks with discrete delays and a conical structure

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  • Chen, Jing
  • Xiao, Min
  • Wu, Xiaoqun
  • Wang, Zhengxin
  • Cao, Jinde

Abstract

In this paper, the stability and Hopf bifurcation problems on a class of high-order reaction–diffusion neural networks are investigated, where the conical structure and signal transmission delays are introduced to make the model more accurate. By the linear stability analysis, Hopf bifurcation theory and Turing instability theorem, some criteria on the local stability and Hopf bifurcation of this system are established by selecting the time delay as bifurcation parameter. Especially, the Coates formula and the holistic element method are taken to determine the critical value, at which the purely imaginary root appears in the associated high-degree characteristic equation. On the other hand, the effects of diffusion terms on the spatial distribution of periodic solutions are explored. New sufficient conditions are derived to guarantee the occurrence of spatially homogeneous periodic solutions. Finally, some numerical examples are provided to validate the main results. It is found that the critical value can also be affected by the network size and the self-feedback rate.

Suggested Citation

  • Chen, Jing & Xiao, Min & Wu, Xiaoqun & Wang, Zhengxin & Cao, Jinde, 2022. "Spatiotemporal dynamics on a class of (n+1)-dimensional reaction–diffusion neural networks with discrete delays and a conical structure," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008542
    DOI: 10.1016/j.chaos.2022.112675
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    References listed on IDEAS

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