Dynamics of a harvested cyanobacteria-fish model with modified Holling type Ⅳ functional response

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.2023561

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 7: 12599-12624. doi: 10.3934/mbe.2023561

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Dynamics of a harvested cyanobacteria-fish model with modified Holling type Ⅳ functional response

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

Academic Editor: Sheldon Wang

Received: 17 February 2023 Revised: 12 April 2023 Accepted: 09 May 2023 Published: 26 May 2023

In this paper, considering the aggregation effect and Allee effect of cyanobacteria populations and the harvesting of both cyanobacteria and fish by human beings, a new cyanobacteria-fish model with two harvesting terms and a modified Holling type Ⅳ functional response function is proposed. The main purpose of this paper is to further elucidate the influence of harvesting terms on the dynamic behavior of a cyanobacteria-fish model. Critical conditions for the existence and stability of several interior equilibria are given. The economic equilibria and the maximum sustainable total yield problem are also studied. The model exhibits several bifurcations, such as transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation. It is concluded from a biological perspective that the survival mode of cyanobacteria and fish can be determined by the harvesting terms. Finally, concrete examples of our model are given through numerical simulations to verify and enrich the theoretical results.
- cyanobacteria-fish model,
- Allee effect,
- harvesting,
- aggregation effect,
- bifurcation
Citation: Shengyu Huang, Hengguo Yu, Chuanjun Dai, Zengling Ma, Qi Wang, Min Zhao. Dynamics of a harvested cyanobacteria-fish model with modified Holling type Ⅳ functional response[J]. Mathematical Biosciences and Engineering, 2023, 20(7): 12599-12624. doi: 10.3934/mbe.2023561

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Abstract

In this paper, considering the aggregation effect and Allee effect of cyanobacteria populations and the harvesting of both cyanobacteria and fish by human beings, a new cyanobacteria-fish model with two harvesting terms and a modified Holling type Ⅳ functional response function is proposed. The main purpose of this paper is to further elucidate the influence of harvesting terms on the dynamic behavior of a cyanobacteria-fish model. Critical conditions for the existence and stability of several interior equilibria are given. The economic equilibria and the maximum sustainable total yield problem are also studied. The model exhibits several bifurcations, such as transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation. It is concluded from a biological perspective that the survival mode of cyanobacteria and fish can be determined by the harvesting terms. Finally, concrete examples of our model are given through numerical simulations to verify and enrich the theoretical results.

References

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