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Bifurcation Analysis for a Delayed Diffusive Logistic Population Model in the Advective Heterogeneous Environment

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Abstract

In this paper, we investigate a delayed reaction–diffusion–advection equation, which models the population dynamics in the advective heterogeneous environment. The existence of the nonconstant positive steady state and associated Hopf bifurcation are obtained. A weighted inner product associated with the advection rate is introduced to compute the normal forms, which is the main difference between Hopf bifurcation for delayed reaction–diffusion–advection model and that for delayed reaction–diffusion model. Moreover, we find that the spatial scale and advection can affect Hopf bifurcation in the heterogenous environment.

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Acknowledgements

The authors are grateful to the anonymous referees for their helpful comments and valuable suggestions which have improved the presentation of the paper.

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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 & Xue Zhang

  2. School of Mathematics and Data, Foshan University, Foshan, 528000, Guangdong, People’s Republic of China

    Junjie Wei

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  1. Shanshan Chen
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Correspondence to Junjie Wei.

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

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Chen, S., Wei, J. & Zhang, X. Bifurcation Analysis for a Delayed Diffusive Logistic Population Model in the Advective Heterogeneous Environment. J Dyn Diff Equat 32, 823–847 (2020). https://doi.org/10.1007/s10884-019-09739-0

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  • DOI: https://doi.org/10.1007/s10884-019-09739-0

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