The Effect of Mutual Interaction and Harvesting on Food Chain Model

Authors

  • Sarab Kazim Hassan Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
  • Shireen Rasool Jawad Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq https://orcid.org/0000-0002-3090-8357

DOI:

https://doi.org/10.24996/ijs.2022.63.6.29

Keywords:

Food chain model, Prey-predator model, Mutual interaction, Harvesting, Stability

Abstract

       This paper treats the interactions among four population species. The system includes one mutuality prey, one harvested prey and two predators. The four species interaction can be described as a food chain, where the first prey helps the second harvested prey. The first and the second predator attack the first and the second prey, respectively, according to Lotka-Volterra type functional responses. The model is formulated using differential equations. One equilibrium point of the model is found and analysed to reveal a threshold that will allow the coexistence of all species. All other equilibrium points of the system are located, with their local and global stability being assessed. To back up the conclusions of the mathematical analysis, a numerical simulation examination of the model is carried out. The system's coexistence can be achieved as long as the harvesting rate of the prey population is lower than its intrinsic growth rate.

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Published

2022-06-30

Issue

Section

Mathematics

How to Cite

The Effect of Mutual Interaction and Harvesting on Food Chain Model. (2022). Iraqi Journal of Science, 63(6), 2641-2649. https://doi.org/10.24996/ijs.2022.63.6.29

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