The dynamics of an aquatic ecological model with aggregation, Fear and Harvesting Effects

Ashraf Adnan Thirthar; Salam J. Majeed; Kamal Shah; Thabet Abdeljawad; Ashraf Adnan Thirthar; Salam J. Majeed; Kamal Shah; Thabet Abdeljawad

doi:10.3934/math.20221018

AIMS Mathematics

2022, Volume 7, Issue 10: 18532-18552. doi: 10.3934/math.20221018

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The dynamics of an aquatic ecological model with aggregation, Fear and Harvesting Effects

1.
Department of Studies and Planning, University of Fallujah, Anbar, Iraq
2.
Department of Mathematics, Collage of Computer Science and Mathematics, University of Thi-Qar, Iraq
3.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi Arabia
4.
Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000, Khyber Pakhtunkhwa, Pakistan
5.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Received: 17 June 2022 Revised: 23 July 2022 Accepted: 04 August 2022 Published: 18 August 2022
MSC : 92D40, 90C31, 34C23

In this paper, we investigate an aquatic ecological model of microcystis aeruginosa-filter feeding fish and predatory fish model with aggregation effect of microcystis aeruginosa. Fear effect of predatory fish on filter feeding fish and harvesting effect of big fish is considered. Mathematical analysis includes two parts. The first is theoretical part, which includes proving the positive and constraining solutions of the model. Also finding equilibrium points and studying their local stability is included in this part. In addition, analyzing the local bifurcation of equilibrium points and indicating the type of bifurcation is discussed here. On the other hand, the second part contains the numerical simulation of all the theoretical results, where we compare the numerical values of the conditions obtained in the theoretical part.
- ecology,
- fear effect,
- harvesting,
- local stability,
- local bifurcation
Citation: Ashraf Adnan Thirthar, Salam J. Majeed, Kamal Shah, Thabet Abdeljawad. The dynamics of an aquatic ecological model with aggregation, Fear and Harvesting Effects[J]. AIMS Mathematics, 2022, 7(10): 18532-18552. doi: 10.3934/math.20221018

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Abstract

In this paper, we investigate an aquatic ecological model of microcystis aeruginosa-filter feeding fish and predatory fish model with aggregation effect of microcystis aeruginosa. Fear effect of predatory fish on filter feeding fish and harvesting effect of big fish is considered. Mathematical analysis includes two parts. The first is theoretical part, which includes proving the positive and constraining solutions of the model. Also finding equilibrium points and studying their local stability is included in this part. In addition, analyzing the local bifurcation of equilibrium points and indicating the type of bifurcation is discussed here. On the other hand, the second part contains the numerical simulation of all the theoretical results, where we compare the numerical values of the conditions obtained in the theoretical part.

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