International Journal of Nonlinear Analysis and Applications

The dynamics of a modified Holling-Tanner prey-predator model with wind effect

Document Type : Research Paper

Authors

1 Department of Mathematics, College of Science, University of Baghdad, Iraq

2 Department of Mathematics, Brunel University London, Uxbridge, United Kingdom

Abstract

Wind flow is one of the biosphere components that could change the amount of predation. This paper suggests and analyses a prey-predator model including wind in the predation task. The Holling-Tanner functional response has been considered to illustrate the global dynamics of the proposed model, considering the change in wind intensity. The persistence conditions are provided to reveal a threshold that will allow the coexistence of all species. Numerical simulations are provided to back up the theoretical analysis. The system’s coexistence can be achieved in abundance as long as the wind flow increases.

Keywords

[1] C. Arancibia-Ibarra, The basins of attraction in a modified May–Holling–Tanner predator–prey model with Allee
affect, Nonlinear Anal. 185 (2019) 15–28.
[2] P. Feng and Y. Kang, Dynamics of a modified leslie–gower model with double allee effects, Nonlinear Dyn. 80(1)
(2015) 1051–1062.
[3] H.I. Freedman, Deterministic Mathematical Models in Population Ecology, Marcel Dekker Incorporated, 1980.
[4] T.C. Gard and T.G. Hallam, Persistence in food webs—I Lotka-Volterra food chains, Bull. Math. Biol. 41(6)
(1979) 877–891.
[5] C.S. Holling, The functional response of invertebrate predators to prey density, Mem. Entomol. Soc. 98(S48)
(1966) 5–86.
[6] S. Jawad, Stability Analysis of Prey-Predator Models with a Reserved Zone and Stage Structure, The University
of Baghdad, College of Science, Department of Mathematics, 2009.
[7] S. Jawad, Modelling, Dynamics and Analysis of Multi-Species Systems with Prey Refuge, Doctoral Dissertation,
Brunel University London, 2018.[8] E. Klimczuk, L. Halupka, B. Czy˙z, M. Borowiec, J.J. Nowakowski and H. Sztwiertnia, Factors driving variation
in biparental incubation behaviour in the reed warbler Acrocephalus scirpaceus, Ardea. 103(1) (2015) 51–59.
[9] P.H. Leslie, Some further notes on the use of matrices in population mathematics, Biometrika 35(3/4) (1948)
213–245.
[10] A.J. Lotka, Elements of physical biology, Sci. Prog. Twent. 21(82) (1926) 341–343.
[11] T.R. McVicar et al., Global review and synthesis of trends in observed terrestrial near-surface wind speeds: Implications for evaporation, J. Hydrol. 416 (2012) 182–205.
[12] R.K. Naji and S.R. Jawad, The dynamics of prey-predator model with a reserved zone, World J. Model. Simul.
12(3) (2016) 175–188.
[13] M. M. Nomdedeu, C. Willen, A. Schieffer and H. Arndt, Temperature-dependent ranges of coexistence in a model
of a two-prey-one-predator microbial food web, Mar. Biol. 159(11) (2012) 2423–2430.
[14] J. Roy, D. Barman and S. Alam, Role of fear in a predator-prey system with ratio-dependent functional response
in deterministic and stochastic environment, Biosyst. 197 (2020).
[15] R.N. Shalan, S.R. Jawad and A.H. Lafta, Stability of the discrete stage–structure prey–predator model, J. Southwest Jiaotong Univ. 55(1) (2020).
International Journal of Nonlinear Analysis and Applications
Volume 12, Special Issue
December 2021
Pages 2203-2210
  • Receive Date: 07 October 2021
  • Revise Date: 22 November 2021
  • Accept Date: 09 December 2021