Dynamic analysis of a modified algae and fish model with aggregation and Allee effect

Shengyu Huang; Hengguo Yu; Chuanjun Dai; Zengling Ma; Qi Wang; Min Zhao; Shengyu Huang; Hengguo Yu; Chuanjun Dai; Zengling Ma; Qi Wang; Min Zhao

doi:10.3934/mbe.2022169

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 4: 3673-3700. doi: 10.3934/mbe.2022169

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Dynamic analysis of a modified algae and fish model with aggregation 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

Academic Editor: Yang Kuang

Received: 04 November 2021 Revised: 04 January 2022 Accepted: 25 January 2022 Published: 08 February 2022

In the paper, under the stress of aggregation and reproduction mechanism of algae, we proposed a modified algae and fish model with aggregation and Allee effect, its main purpose was to further ascertain the dynamic relationship between algae and fish. Several critical conditions were investigated to guarantee the existence and stabilization of all possible equilibrium points, and ensure that the model could undergo transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation and B-T bifurcation. Numerical simulation results of related bifurcation dynamics were provided to verify the feasibility of theoretical derivation, and visually demonstrate the changing trend of the dynamic relationship. Our results generalized and improved some known results, and showed that the aggregation and Allee effect played a vital role in the dynamic relationship between algae and fish.
- aquatic ecological model,
- Allee effect,
- aggregation effect,
- equilibrium point,
- bifurcation
Citation: Shengyu Huang, Hengguo Yu, Chuanjun Dai, Zengling Ma, Qi Wang, Min Zhao. Dynamic analysis of a modified algae and fish model with aggregation and Allee effect[J]. Mathematical Biosciences and Engineering, 2022, 19(4): 3673-3700. doi: 10.3934/mbe.2022169

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Abstract

In the paper, under the stress of aggregation and reproduction mechanism of algae, we proposed a modified algae and fish model with aggregation and Allee effect, its main purpose was to further ascertain the dynamic relationship between algae and fish. Several critical conditions were investigated to guarantee the existence and stabilization of all possible equilibrium points, and ensure that the model could undergo transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation and B-T bifurcation. Numerical simulation results of related bifurcation dynamics were provided to verify the feasibility of theoretical derivation, and visually demonstrate the changing trend of the dynamic relationship. Our results generalized and improved some known results, and showed that the aggregation and Allee effect played a vital role in the dynamic relationship between algae and fish.

References

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