Optimal control analysis of a predator-prey model with harvesting and variable carrying capacity

Ibrahim M. Elmojtaba; Amina Al-Sawaii; Mariam Al-Moqbali

doi:10.28919/cmbn/4505

Optimal control analysis of a predator-prey model with harvesting and variable carrying capacity

Ibrahim M. Elmojtaba^*, Amina Al-Sawaii, Mariam Al-Moqbali

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we developed and fully analysed a mathematical model for the dynamics of predator and prey where the carrying capacity is considered to be a logistically increasing function of time, and both populations are under harvesting. Our results showed that if the harvesting rate is high then both populations could go to extinction. We also showed that the system undergoes Hopf bifurcation when the harvesting rate of the prey crosses a critical value; in fact the stability of the system changes with the change of the values of the prey harvesting rate. Optimal harvesting is shown to give a high yield and keep both population away from extension.

Original language	English
Article number	12
Pages (from-to)	1-19
Number of pages	19
Journal	Communications in Mathematical Biology and Neuroscience
Volume	2020
DOIs	https://doi.org/10.28919/cmbn/4505
Publication status	Published - 2020
Externally published	Yes

Keywords

Hopf bifurcation
Local stability
Optimal harvesting
Predator-prey model
Variable carrying capacity

ASJC Scopus subject areas

Neuroscience(all)
Biochemistry, Genetics and Molecular Biology(all)
Applied Mathematics

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title = "Optimal control analysis of a predator-prey model with harvesting and variable carrying capacity",

abstract = "In this paper, we developed and fully analysed a mathematical model for the dynamics of predator and prey where the carrying capacity is considered to be a logistically increasing function of time, and both populations are under harvesting. Our results showed that if the harvesting rate is high then both populations could go to extinction. We also showed that the system undergoes Hopf bifurcation when the harvesting rate of the prey crosses a critical value; in fact the stability of the system changes with the change of the values of the prey harvesting rate. Optimal harvesting is shown to give a high yield and keep both population away from extension.",

keywords = "Hopf bifurcation, Local stability, Optimal harvesting, Predator-prey model, Variable carrying capacity",

author = "Elmojtaba, {Ibrahim M.} and Amina Al-Sawaii and Mariam Al-Moqbali",

note = "Funding Information: The authors are supported through grant NO. IG/SCI/DOMS/18/03 from Sultan Qaboos University. Publisher Copyright: {\textcopyright} 2020 the author(s).",

year = "2020",

doi = "10.28919/cmbn/4505",

language = "English",

volume = "2020",

pages = "1--19",

journal = "Communications in Mathematical Biology and Neuroscience",

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T1 - Optimal control analysis of a predator-prey model with harvesting and variable carrying capacity

AU - Elmojtaba, Ibrahim M.

AU - Al-Sawaii, Amina

AU - Al-Moqbali, Mariam

PY - 2020

Y1 - 2020

N2 - In this paper, we developed and fully analysed a mathematical model for the dynamics of predator and prey where the carrying capacity is considered to be a logistically increasing function of time, and both populations are under harvesting. Our results showed that if the harvesting rate is high then both populations could go to extinction. We also showed that the system undergoes Hopf bifurcation when the harvesting rate of the prey crosses a critical value; in fact the stability of the system changes with the change of the values of the prey harvesting rate. Optimal harvesting is shown to give a high yield and keep both population away from extension.

AB - In this paper, we developed and fully analysed a mathematical model for the dynamics of predator and prey where the carrying capacity is considered to be a logistically increasing function of time, and both populations are under harvesting. Our results showed that if the harvesting rate is high then both populations could go to extinction. We also showed that the system undergoes Hopf bifurcation when the harvesting rate of the prey crosses a critical value; in fact the stability of the system changes with the change of the values of the prey harvesting rate. Optimal harvesting is shown to give a high yield and keep both population away from extension.

KW - Hopf bifurcation

KW - Local stability

KW - Optimal harvesting

KW - Predator-prey model

KW - Variable carrying capacity

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JO - Communications in Mathematical Biology and Neuroscience

JF - Communications in Mathematical Biology and Neuroscience

M1 - 12

ER -

Optimal control analysis of a predator-prey model with harvesting and variable carrying capacity

Abstract

Keywords

ASJC Scopus subject areas

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