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Hopf Bifurcation of a Delayed Single Population Model with Patch Structure

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Abstract

In this paper, we show the existence of a Hopf bifurcation in a delayed single population model with patch structure. The effect of the dispersal rate on the Hopf bifurcation is considered. Especially, if each patch is favorable for the species, we show that when the dispersal rate tends to zero, the limit of the Hopf bifurcation value is the minimum of the “local” Hopf bifurcation values over all patches. On the other hand, when the dispersal rate tends to infinity, the Hopf bifurcation value tends to that of the “average” model.

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, Weihai, 264209, Shandong, People’s Republic of China

    Shanshan Chen & Junjie Wei

  2. Department of Basic Education, Harbin University of Science and Technology, Rongcheng Campus, Weihai, 264300, Shandong, People’s Republic of China

    Zuolin Shen

  3. School of Science, Jimei University, Xiamen, 361021, Fujian, People’s Republic of China

    Junjie Wei

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  1. Shanshan Chen
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  2. Zuolin Shen
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  3. Junjie Wei
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Correspondence to Shanshan Chen.

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This research is supported by the National Natural Science Foundation of China (No. 11771109) and Shandong Provincial Natural Science Foundation of China (No. ZR2020YQ01).

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Chen, S., Shen, Z. & Wei, J. Hopf Bifurcation of a Delayed Single Population Model with Patch Structure. J Dyn Diff Equat 35, 1457–1487 (2023). https://doi.org/10.1007/s10884-021-09946-8

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  • DOI: https://doi.org/10.1007/s10884-021-09946-8

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