International Journal of Nonlinear Analysis and Applications
A qualitative study of an Eco-Toxicant model with Anti-Predator behavior
Document Type : Research Paper
Authors
Department of Mathematics, College of Science, University of Baghdad, Iraq
Abstract
In this study, a mathematical model consisting of four species: first prey and second prey with stage structure and predator in the presence of toxicity and anti-predator has been proposed and studied using the functional response Holling's type IV and Lotka Volttra. The solution's existence, uniqueness, and boundedness have all been studied. All possible equilibrium points have been identified. The stability of this model has been studied. Finally, numerical simulations have been used to verify our analytical results.
Keywords
311–326.
[2] M. Bandyopadhyay and J. Chattopadhyay, Ratio-dependent predator-prey model: Effect of environmental fluctuation and stability, Nonlinearity, 18 (2005) 913-936.
[3] M. Banerjee, Self-replication of spatial patterns in a ratio-dependent predator-prey model, Math. Comput. Model.
51 (2010) 44–52.
[4] J. Chattopadhyay, Effect of toxic substances on a two-species competitive system, Eco. Model. 84 (1996) 287–289.
[5] XU. Conghui, REN. Guojian and YU. Yongguang, Extinction analysis of stochastic predator prey system with
stage structure and Crowley-Martin functional response, Bio. Stat. Mech. 21 (2019) 252.
[6] H. I. Freedman and J. B., models for the effect of toxicant in single-species and predator-prey systems, J. Math.
Bio. 30 (1991) 15–30.
[7] J. K. Hale, Ordinary Differential Equation, Wiley-Interscience, New York, 1969.
[8] T. G. Hallam and J. T. Deluna, Effects of toxicant on populations: qualitative approach III. Environmental and
food chain pathways, J. Theo. Bio. 109 (1984) 411–429.
[9] T. G. Hallam, C. E. Clark and R. R. Lassite, effects of toxicants on populations: A qualitative approach I.
Equilibrium environmental exposure, Eco. Model. 8 (1983) 291–304.[10] A. A. Majeed and M. H. Ismaeel, The dynamical behavior of stage structured prey- predator model in the presence
of harvesting and toxin, J. Southwest Jiaotong Univ. 54(6) (2019) 1–8.
[11] A. A. Majeed and M.A. Latf, The food web prey-predator with toxin, AIP Conf. Proc. 2292 (2020) 030015.
[12] A.A. Majeed and A.J. Kadhim, The impact of toxicant on the food chain ecological model, AIP Conf. Proc. 2292
(2020) 04001.
[13] A.A. Majeed, Local bifurcation and persistence of an ecological system consisting of a predator and stage structured
prey, Iraqi J. Sci. 54 (2013) 696–705.
[14] 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, Inf. Med. Unlock. 10 (2018) 50–57.
[15] P. Panja, S. K. Mondal and J. Chattopadhyay, Dynamic effects of anti-predator behavior of adult prey in a
prey-prey model with a ratio-dependent functional response, Numerical Alg. Cont. Opt. 11 (2021) 21–22.
[16] D .Savitrt, Dynamic analysis of a predator-fighting model on the intermediate predator with ratio-dependent
functional responses, J. Phys. Conf. Ser., 953 (2018) 1–7.
[17] B. Tang and Y. Xiao,Bifurcation analysis of a predator - prey model with anti-predator behavior, Chaos, Solit.
Fract. 70 (2015) 58–68.
)
Volume 12, Issue 2
November 2021Pages 1861-1882
- Receive Date: 12 March 2021
- Revise Date: 02 July 2021
- Accept Date: 13 July 2021