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Volume 35, Issue 2
The Qualitative Analysis of a Two Species Amensalism Model with Non-Monotonic Functional Response and Allee Effect on Second Species

Xinyu Guan & Hang Deng

Ann. Appl. Math., 35 (2019), pp. 126-138.

Published online: 2020-08

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  • Abstract

In this paper, we present a two species amensalism model with non-monotonic functional response and Allee effect on second species. Local and global stability of the boundary and interior equilibrium are investigated. By introducing the Allee effect, we show that the boundary equilibrium have changed from unstable node and saddle into saddle-node. Also, the system subject to an Allee effect has increased the time of reach to its stable steady-state solution, but has no influence on the final density of the two species. Our results are supported by numeric simulations.

  • Keywords

amensalism model, Allee effect, non-monotonic functional response, global stability.

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COPYRIGHT: © Global Science Press

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@Article{AAM-35-126, author = {Guan , Xinyu and Deng , Hang}, title = {The Qualitative Analysis of a Two Species Amensalism Model with Non-Monotonic Functional Response and Allee Effect on Second Species}, journal = {Annals of Applied Mathematics}, year = {2020}, volume = {35}, number = {2}, pages = {126--138}, abstract = {

In this paper, we present a two species amensalism model with non-monotonic functional response and Allee effect on second species. Local and global stability of the boundary and interior equilibrium are investigated. By introducing the Allee effect, we show that the boundary equilibrium have changed from unstable node and saddle into saddle-node. Also, the system subject to an Allee effect has increased the time of reach to its stable steady-state solution, but has no influence on the final density of the two species. Our results are supported by numeric simulations.

}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aam/18071.html} }
TY - JOUR T1 - The Qualitative Analysis of a Two Species Amensalism Model with Non-Monotonic Functional Response and Allee Effect on Second Species AU - Guan , Xinyu AU - Deng , Hang JO - Annals of Applied Mathematics VL - 2 SP - 126 EP - 138 PY - 2020 DA - 2020/08 SN - 35 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/aam/18071.html KW - amensalism model, Allee effect, non-monotonic functional response, global stability. AB -

In this paper, we present a two species amensalism model with non-monotonic functional response and Allee effect on second species. Local and global stability of the boundary and interior equilibrium are investigated. By introducing the Allee effect, we show that the boundary equilibrium have changed from unstable node and saddle into saddle-node. Also, the system subject to an Allee effect has increased the time of reach to its stable steady-state solution, but has no influence on the final density of the two species. Our results are supported by numeric simulations.

Xinyu Guan & Hang Deng. (2020). The Qualitative Analysis of a Two Species Amensalism Model with Non-Monotonic Functional Response and Allee Effect on Second Species. Annals of Applied Mathematics. 35 (2). 126-138. doi:
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