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Stability and Bifurcation Analysis of an Amensalism Model with Weak Allee Effect

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Abstract

In this paper, an amensalism model with weak Allee effect is proposed. The existence and stability of all possible positive equilibria and the possible boundary equilibria of the system are investigated. We also prove that there are two saddle-node bifurcations under suitable conditions by Sotomayor’s theorem. An example with its numeric simulations are given to verify our main results.

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Acknowledgements

The authors would like to thank Zhenliang Zhu for useful discussion during the period of writing this paper.

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Authors and Affiliations

  1. School of Electronic and Information Engineering, Fuqing Branch of Fujian Normal University, Fuqing, 350300, Fujian, China

    Zhen Wei

  2. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Yonghui Xia

  3. Department of Mathematics, Swinburne University of Technology, Hawthorn, VIC, 3122, Australia

    Tonghua Zhang

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  1. Zhen Wei
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  2. Yonghui Xia
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  3. Tonghua Zhang
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All authors contributed equally to the writing of this paper.

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Correspondence to Yonghui Xia.

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The research was supported by Fujian Provincial Middle and Young Teachers Education and Research Project (JAT170682), the National Natural Science Foundation of China under Grant (No. 11931016), Natural Science Foundation of Zhejiang Province under Grant (No. LY20A010016), start-up fund of Huaqiao University (Z16J0039).

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Wei, Z., Xia, Y. & Zhang, T. Stability and Bifurcation Analysis of an Amensalism Model with Weak Allee Effect. Qual. Theory Dyn. Syst. 19, 23 (2020). https://doi.org/10.1007/s12346-020-00341-0

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