Dynamical analysis of an aquatic amensalism model with non-selective harvesting and Allee effect

Huanyi Liu; Hengguo Yu; Chuanjun Dai; Zengling Ma; Qi Wang; Min Zhao; Huanyi Liu; Hengguo Yu; Chuanjun Dai; Zengling Ma; Qi Wang; Min Zhao

doi:10.3934/mbe.2021437

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 6: 8857-8882. doi: 10.3934/mbe.2021437

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Dynamical analysis of an aquatic amensalism model with non-selective harvesting and Allee effect

1.
Key Laboratory for Subtropical Oceans & Lakes Environment and Biological Resources Utilization Technology of Zhejiang, Wenzhou University, Wenzhou, Zhejiang, 325035, China
2.
School of Mathematics and Physics, Wenzhou University, Wenzhou, Zhejiang, 325035, China
3.
School of Life and Environmental Science, Wenzhou University, Wenzhou, Zhejiang, 325035, China

Received: 10 June 2021 Accepted: 07 October 2021 Published: 15 October 2021

In this paper, in order to explore the inhibition mechanism of algicidal bacteria on algae, we constructed an aquatic amensalism model with non-selective harvesting and Allee effect. Mathematical works mainly gave some critical conditions to guarantee the existence and stability of equilibrium points, and derived some threshold conditions for saddle-node bifurcation and transcritical bifurcation. Numerical simulation works mainly revealed that non-selective harvesting played an important role in amensalism dynamic relationship. Meanwhile, we proposed some biological explanations for transcritical bifurcation and saddle-node bifurcation from the aspect of algicidal bacteria controlling algae. Finally, all these results were expected to be useful in studying dynamical behaviors of aquatic amensalism ecosystems and biological algae controlling technology.
- amensalism model,
- Allee effect,
- harvest,
- transcritical bifurcation,
- saddle-node bifurcation
Citation: Huanyi Liu, Hengguo Yu, Chuanjun Dai, Zengling Ma, Qi Wang, Min Zhao. Dynamical analysis of an aquatic amensalism model with non-selective harvesting and Allee effect[J]. Mathematical Biosciences and Engineering, 2021, 18(6): 8857-8882. doi: 10.3934/mbe.2021437

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Abstract

In this paper, in order to explore the inhibition mechanism of algicidal bacteria on algae, we constructed an aquatic amensalism model with non-selective harvesting and Allee effect. Mathematical works mainly gave some critical conditions to guarantee the existence and stability of equilibrium points, and derived some threshold conditions for saddle-node bifurcation and transcritical bifurcation. Numerical simulation works mainly revealed that non-selective harvesting played an important role in amensalism dynamic relationship. Meanwhile, we proposed some biological explanations for transcritical bifurcation and saddle-node bifurcation from the aspect of algicidal bacteria controlling algae. Finally, all these results were expected to be useful in studying dynamical behaviors of aquatic amensalism ecosystems and biological algae controlling technology.

References

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