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Symmetry-breaking bifurcations in a delayed reaction–diffusion equation

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Abstract

This paper is concerned with a delayed reaction–diffusion equation on a unit disk. By means of the singularity theory and Lyapunov–Schmidt reduction, we not only derive universal conclusions about the existence of inhomogeneous steady-state solutions and the equivariant Hopf bifurcation theorems, but also obtain some more extraordinary properties of bifurcating solutions, which are produced by the radial symmetry through abstract methods based on the Lie group representation theory. Meanwhile, we illustrate our results by an application to a population model with a time delay. Furthermore, the methods established in this paper are applicable to specific delayed reaction–diffusion models with other symmetries.

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Acknowledgements

This work has been supported by the Natural Science Foundation of China (Grant No. 12071446) and the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (Grant No. CUGST2).

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  1. School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, Hubei, People’s Republic of China

    Xiaowei Qu & Shangjiang Guo

  2. Center for Mathematical Sciences, China University of Geosciences, Wuhan, 430074, Hubei, People’s Republic of China

    Shangjiang Guo

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  1. Xiaowei Qu
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Qu, X., Guo, S. Symmetry-breaking bifurcations in a delayed reaction–diffusion equation. Z. Angew. Math. Phys. 74, 76 (2023). https://doi.org/10.1007/s00033-023-01968-0

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