Predator and n-classes-of-prey model incorporating extended Holling type Ⅱ functional response for n different prey species

Saiwan Fatah; Arkan Mustafa; Shilan Amin; Saiwan Fatah; Arkan Mustafa; Shilan Amin

doi:10.3934/math.2023291

AIMS Mathematics

2023, Volume 8, Issue 3: 5779-5788. doi: 10.3934/math.2023291

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Predator and n-classes-of-prey model incorporating extended Holling type Ⅱ functional response for n different prey species

Department of Mathematics, College of Education, University of Sulaimani, Kurdistan Region Iraq

Received: 03 October 2022 Revised: 21 November 2022 Accepted: 13 December 2022 Published: 26 December 2022
MSC : 92D25, 34L99

In this paper, the Holling type Ⅱ functional response extended for n different species of prey and the dynamics of interactions between one predator species and its n different classes of prey are modeled. Positivity, boundedness and permanence of all solutions of the model are proved. An ecological threshold parameter for the predator free equilibrium point of the model is established. Local stability and global stability of the predator free equilibrium point are discussed. Furthermore, we also studied that the reproduction number R₀ determines whether the equilibrium points are asymptotically stable or unstable. In addition, the model was solved numerically to confirm the analytical results.
- Holling type Ⅱ functional response,
- ecological reproduction number,
- stability analysis
Citation: Saiwan Fatah, Arkan Mustafa, Shilan Amin. Predator and n-classes-of-prey model incorporating extended Holling type Ⅱ functional response for n different prey species[J]. AIMS Mathematics, 2023, 8(3): 5779-5788. doi: 10.3934/math.2023291

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Abstract

In this paper, the Holling type Ⅱ functional response extended for n different species of prey and the dynamics of interactions between one predator species and its n different classes of prey are modeled. Positivity, boundedness and permanence of all solutions of the model are proved. An ecological threshold parameter for the predator free equilibrium point of the model is established. Local stability and global stability of the predator free equilibrium point are discussed. Furthermore, we also studied that the reproduction number R₀ determines whether the equilibrium points are asymptotically stable or unstable. In addition, the model was solved numerically to confirm the analytical results.

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