Volume 24 • Issue 3 • PP: 280-295 • 2024
The Impact of Anti-Predator Behavior and Toxicant on An Ecological Neutrosophic Model
View PDF Abstract
This paper discusses a neutrosophic mathematical model consisting of three nonlinear ordinary differential equations describing the interaction between two prey and a predator with the use of function response Holling's type IV and Lotka Volttra. It appears that the first prey has a way to defend itself by using the toxic substance directly to the predator, as well as the effect of the predator on the toxic substance. The conditions for the existence of the solution and the uniqueness of the boundaries were discussed, and then the different equilibrium points and the stability of the system around the equilibrium points were analyzed. The Lyapunov function was used to study the global dynamics of this proposed model. Finally, numerical simulations were performed to show the analytical results.
Keywords
References
[1] Allman ES, Rhodes JA. Mathematical models in biology: an introduction. Cambridge University Press; 2004.
[2] Abd A, Naji RK. The impact of alternative resources and fear on the dynamics of the food chain. International Journal of Nonlinear Analysis and Applications 2021;12:2207–34.
[3] Kareem HS, Majeed AA. A qualitative study of an Eco-Toxicant model with Anti-Predator behavior. International Journal of Nonlinear Analysis and Applications 2021;12:1861–82.
[4] Dawud S, Jawad S. Stability analysis of a competitive ecological system in a polluted environment. Commun Math Biol Neurosci 2022;2022:Article-ID.
[5] Hassan SK, Jawad SR. The Effect of Mutual Interaction and Harvesting on Food Chain Model. Iraqi Journal of Science 2022:2641–9.
[6] Jawad SR, Al Nuaimi M. Persistence and bifurcation analysis among four species interactions with the influence of competition, predation and harvesting. Iraqi Journal of Science 2023:1369–90.
[7] Maghool FH, Naji RK. The effect of fear on the dynamics of two competing prey-one predator system involving intra-specific competition. Commun Math Biol Neurosci 2022;2022:Article-ID.
[8] Maghool FH, Naji RK. Chaos in the three-species Sokol-Howell food chain system with fear. Commun Math Biol Neurosci 2022;2022:Article-ID.
[9] Majeed AA. Qualitative study of an eco-epidemiological model with anti-predator and migration presence. International Journal of Nonlinear Analysis and Applications 2022;13:889–99.
[10] Banerjee M, Venturino E. A phytoplankton–toxic phytoplankton–zooplankton model. Ecological Complexity 2011;8:239–48.
[11] Arditi R, Ginzburg LR. Coupling in predator-prey dynamics: ratio-dependence. Journal of Theoretical Biology 1989;139:311–26.
[12] Mukherjee M, Pal D, Mahato SK, Bonyah E. Prey–predator optimal harvesting mathematical model in the presence of toxic prey under interval uncertainty. Scientific African 2023;21:e01837.
[13] Kumar P, Raj S. Modelling the Effect of Toxin Producing Prey on Predator Population using Delay Differential Equations. Journal of Physics: Conference Series, vol. 2267, IOP Publishing; 2022, p. 12077.
[14] Talib RH, Helal MM, Naji RK. The Dynamics of the Aquatic Food Chain System in the Contaminated Environment. Iraqi Journal of Science 2022:2173–93.
[15] Hale JK. Ordinary differential equations. Courier Corporation; 2009.
[16] S. Salem, Z. Khan, H. Ayed, A. Brahmia, and A. Amin, “The Neutrosophic Lognormal Model in Lifetime Data Analysis: Properties and Applications,” J. Funct. Spaces, vol. 2021, 2021, doi: 10.1155/2021/6337759.
[17] Z. Khan, A. Al-Bossly, M. M. A. Almazah, and F. S. Alduais, “On Statistical Development of Neutrosophic Gamma Distribution with Applications to Complex Data Analysis,” Complexity, vol. 2021, 2021, doi: 10.1155/2021/3701236.
[18] W. Q. Duan, Z. Khan, M. Gulistan, and A. Khurshid, “Neutrosophic Exponential Distribution: Modeling and Applications for Complex Data Analysis,” Complexity, vol. 2021, 2021, doi: 10.1155/2021/5970613.
[19] C. Granados and J. Sanabria, “On Independence Neutrosophic Random Variables,” Neutrosophic Sets Syst., vol. 47, 2021.
Cite This Article
Choose your preferred format