Effect of an amount of extra food on the dynamics of a food -web model with modified Holling type II functional response

Authors

  • Arkan Mustafa Department of Mathematics, College of Education, University of Sulaimani, IRAQ
  • Karzan Abdurahman Hamzah Department of Mathematics, College of Education, University of Sulaimani, IRAQ

DOI:

https://doi.org/10.31185/wjps.672

Keywords:

Food web, Extra food, Functional response, Stability analysis, Hopf-bifurcation

Abstract

This paper deals with studding the effect of an amount of additional food supplies on the dynamic interaction of three species food-web, the species are, prey, intermediate predators and top predators. The top predator species predate both prey species and intermediate predator species according to extended Holling type II functional response for two prey species. Firstly it is proved that the model solutions are bounded under certain condition. All biological possible steady states are explored, and their local stability is analyzed based on the sample parameters. Critical values that make the occurrence of Hopf-bifurcation of the model near intermediate predators-free and top predator-free steady states are determined. Finally, with the help of MATLAB, it is performed numerical simulations to support the evidence of the analytical results regarding to stability and Hopf- bifurcation , Further it is observed that when the amount of extra food increases, the dynamics of the model may induced a transition from the a stability situation to the state where populations oscillate periodically.

References

Rebelo, P.; Roza, S. An optimal control problem for a predator–prey model with strong and weak preys. Chaos, Solitons and Fractals, 2025, 191.

https://doi.org/10.1016/j.chaos.2024.115838

Fatah, S.; Mustafa, A.; Amin, S. Predator and n-classes-of-prey model incorporating Extended Holling type II functional response for n different prey species. AIMS Mathematics, 2022,8(3), 5779-5788.

https://doi.org/10.3934/math.2023291

Farhan, A.G.; Khalaf, N.S.; Aldhlki ,T.J. Dynamical Behaviors of Four Dimensional Prey-Predator Model. Eur. J. Pure Appl. Math.2023, 16(2), 899-918.

https://doi.org/10.29020/nybg.ejpam.v16i2.4716

Djilali, S.; Ghanbari, B. Dynamical behavior of two predators–one prey model with generalized functional response and time-fractional derivative. Advances in difference Equations, 2021(1), 1–19.

http://dx.doi.org/10.1186/s13662-021-03395-9

Ghosh, U.; Sarkar, S.; Mondal B. Study of stability and bifurcation of three species food chain model with non-monotone functional response. Int. l J. of App and Comp Mathematics, 2021, 7: 1–24.

https://link.springer.com/article/10.1007/s40819-021-01017-2

Numan, H., & Mustafa, A. (2024). Role of Fear and disease on the Dynamics of two prey-one predator model with extended Holling type II functional response. Wasit Journal for Pure Sciences , 3(4), 38-49.

https://doi.org/10.31185/wjps.595

Mishra, S.; Upadhyay, R.K. Exploring the cascading effect of fear on the foraging activities of prey in a three species Agroecosystem .The European Physical Journal Plus,2021, 136, 1–36.

http://dx.doi.org/10.1140/epjp/s13360-021-01936-5

Holling, C.S. Some characteristics of simple types of predation and parasitism1. The canadian entomologist, 1959, 91(7), 385–398.

https://doi.org/10.4039/Ent91385-7

Jha, P.K.; Ghorai, S. Stability of prey-predator model with Holling type response function and selective harvesting. J of Appl and Comp Mathematics,2017; 6(3): 1–7.

http://dx.doi.org/10.4172/2168-9679.1000358

Divya, B.; Kavitha, K. Dynamical Behavior Of Three Species Model With Holling Type Functional Response In The Presence Of Logistic Growth. J of App Science and Eng, 28(1),101-108.

https://doi.org/10.6180/jase.202501_28(1).0010

Khan, A.; Qureshi , S.M.; Alotaibi, A.M.Bifurcation analysis of a three species discrete-time predator-prey model. Alex. Eng. Journal, 2022, 61(10), 7853– 7875.

http://dx.doi.org/10.1016/j.aej.2021.12.068

Khan, A.Q.; Kazmi, S.S.; Alharbi, T.D. Bifurcations of a three-species prey-predator system with scavenger. Ain Shams Engineering Journal, 2022, 14(11).

http://dx.doi.org/10.1016/j.asej.2023.102514

Khan, A.Q.; Kazmi, S.S. Dynamical analysis of a three-species discrete biological system with scavenger. J of Comput and App Mathematics ,2024, 440.

http://dx.doi.org/10.1016/j.cam.2023.115644

Diana, A.F.; Widowati, W.; Tjahjana, R.H. Stability analysis of Lotka Volterra model for three species with disease. AIP Conference Proceedings, 2023,2738(1).

https://doi.org/10.1063/5.0140161

Danane, J.; Torres, D.F. Three-Species Predator–Prey Stochastic Delayed Model Driven by Lévy Jumps and with Cooperation Among Prey Species, Mathematics , 2023;11(7).

https://www.mdpi.com/2227-7390/11/7/1595

Pal, S.; Tiwari, P.K.;Misra,A.K.; Wang,H. Fear effect in a three-species food chain model with generalist predator, Math. Bio and Eng. 2024,21(1),1-33.

https://doi.org/10.3934/mbe.2024001

Downloads

Published

2025-03-29

Issue

Vol. 4 No. 1 (2025)

Section

Mathematics

License

Copyright (c) 2025 Arkan Mustafa

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Mustafa, A., & Karzan Abdurahman Hamzah. (2025). Effect of an amount of extra food on the dynamics of a food -web model with modified Holling type II functional response. Wasit Journal for Pure Sciences , 4(1), 76-85. https://doi.org/10.31185/wjps.672

Most read articles by the same author(s)