Hopf Bifurcation of a Delayed Single Population Model with Patch Structure

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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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 (2021). https://doi.org/10.1007/s10884-021-09946-8

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Keywords

  • Hopf bifurcation
  • Patch structure
  • Delay
  • Dispersal

Mathematics Subject Classification

  • 92D30
  • 34K18
  • 34K13
  • 37N25