INFORMATION CHANGE THE WORLD

International Journal of Engineering and Manufacturing(IJEM)

ISSN: 2305-3631 (Print), ISSN: 2306-5982 (Online)

Published By: MECS Press

IJEM Vol.12, No.3, Jun. 2022

The Influence of Stage Structure and Prey Refuge on the Stability of the Predator-Prey Model

Full Text (PDF, 538KB), PP.51-59


Views:2   Downloads:0

Author(s)

Shireen Jawad, Raid Kamel Naji

Index Terms

Predator-prey model, Stage structure, Reserved area, Prey refuge.

Abstract

This paper aims to study the prey refuge impact on the dynamic behaviour of a stage structure predator-prey model. The model consists of four ecological species: prey in the protected and unprotected area and immature and mature predators. It assumes the grown predator can feeds only on the prey in an unreserved area. The conditions that guarantee the existence of the possible fixed points are found. Further, the local stability around all of the equilibria is considered. Then, using the Lyapunov direct method, the essential conditions for the global stability of the equilibria are adopted. Numerical simulations are illustrated to confirm our results. It concluded that the protected area positively affects the system's co-existence.

Cite This Paper

Shireen Jawad, Raid Kamel Naji, " The Influence of Stage Structure  and Prey Refuge on the Stability of the Predator-Prey Model ", International Journal of Engineering and Manufacturing (IJEM), Vol.12, No.3, pp. 51-59, 2022. DOI: 10.5815/ijem.2022.03.05

Reference

[1]S. Jawad, "Study the Dynamics of Commensalism Interaction with Michaels-Menten Type Prey Harvesting," Al-Nahrain J. Sci., vol. 25, no. 1, pp. 45–50, 2022.

[2]S. Jawad, "Stability Analysis of Prey-Predator Models with a Reserved Zone and Stage Structure," Univ. Baghdad, Coll. Sci. Dep. Math., 2009.

[3]A. J. Lotka, "Elements of physical biology," Sci. Prog. Twent. Century, vol. 21, no. 82, pp. 341–343, 1926.

[4]V. Volterra, “Variazioni e fluttuazioni del numero d’individui in specie animali conviventi,” 1926.

[5]S. Jawad, "Modelling, dynamics and analysis of multi-species systems with prey refuge." Brunel University London, 2018.

[6]S. Jawad, D. Sultan, and M. Winter, "The dynamics of a modified Holling-Tanner prey-predator model with wind effect," Int. J. Nonlinear Anal. Appl., vol. 12, no. Special Issue, pp. 2203–2210, 2021.

[7]P. T. Saijnders and M. J. Bazin, “On the stability of food chains,” J. Theor. Biol., vol. 52, no. 1, pp. 121–142, 1975.

[8]B. Dubey, "A prey-predator model with a reserved area," Nonlinear Anal. Model. Control, vol. 12, no. 4, pp. 479–494, 2007.

[9]V. Křivan, "Effects of optimal antipredator behavior of prey on predator–prey dynamics: the role of refuges," Theor. Popul. Biol., vol. 53, no. 2, pp. 131–142, 1998.

[10]J. B. Collings, "Bifurcation and stability analysis of a temperature-dependent mite predator-prey interaction model incorporating a prey refuge," Bull. Math. Biol., vol. 57, no. 1, pp. 63–76, 1995.

[11]S. G. Mortoja, P. Panja, and S. K. Mondal, "Dynamics of a predator-prey model with stage-structure on both species and anti-predator behavior," Informatics Med. unlocked, vol. 10, pp. 50–57, 2018.

[12]V. H. W. Rudolf and K. D. Lafferty, "Stage structure alters how complexity affects stability of ecological networks," Ecol. Lett., vol. 14, no. 1, pp. 75–79, 2011.

[13]N. Mondal, D. Barman, and S. Alam, "Impact of adult predator incited fear in a stage-structured prey–predator model," Environ. Dev. Sustain., vol. 23, no. 6, pp. 9280–9307, 2021.

[14]J. Li, X. Liu, and C. Wei, "The impact of role reversal on the dynamics of predator-prey model with stage structure," Appl. Math. Model., 2021.

[15]T. K. Kar and U. K. Pahari, "Modelling and analysis of a prey–predator system with stage-structure and harvesting," Nonlinear Anal. Real World Appl., vol. 8, no. 2, pp. 601–609, 2007.

[16]S. R. Jawad and R. K. Naji, "Stability Analysis of Stage Structure Prey-Predator Model with a Partially Dependent Predator and Prey Refuge," 2022.