Abstract : It can be difficult to address in practice the dynamics that drive growth, development, survival, and change within an ecological system when a predator and prey species coexist. Mathematical models have helped ecologists better comprehend the system's dynamics. For this purpose, the Lotka-Volterra model, a mathematical framework developed by Alfred J. Lotka and Vito Volterra, is employed. Adaptations were made to the prevailing ecological conditions. The Lotka-Volterra equations are revised as a result of these presumptions. The improved model's equilibrium and stability features are proven. The outcomes were modelled in MATLAB. In order to create the mathematical model, nonlinear ordinary differential equations are used. Biological and chemical toxins are assumed to stunt the development of prey species in mathematical models. We also talk about the model's equilibrium points. Positive definite functions and the Jacobian matrix are taken into account to evaluate the mathematical model. Computational models corroborate the analytical assumptions.
Keywords : Equilibrium points, local and global stability, variational matrix, Lotka volterra model.
Cite : Singh, U. R., Suman, S. K., & Singh, U. (2023). The Impact of Polluted Environment on Population Dynamics of Predator and Prey: Inference of Lotka-Volterra Model (1st ed., pp. 184-190). Noble Science Press. https://doi.org/10.52458/9789388996587.2023.eb.ch35
References :
Chauhan S., Mishra O.P. (2012): “Modeling and a analysis of a single species population with viral infection in polluted environment”, Applied Mathematics, 3: 662-672.
Gao Y., Yao S. (2022): “Dynamical analysis of a modified Leslie–Gower Holling-type II predator-prey stochastic model in polluted environments with interspecific competition and impulsive toxicant input”, Journal of Biological Dynamics, 16(1):840-858.
Hadziabdic V., Mehuljic M., Bekteseviv J. (2017): “Lotka-volterra model with two predators and their prey”, TEM Journal, 6(1):132-136.
Huang Q., Wang H., Lewis M.A. (2015): “The impact of environmental toxins on predator–prey dynamics”, Journal of Theoretical Biology: 378:12-30.
Mishra O.P., Annavarapu R.B. (2016): “A model for the dyanamical study of food chain system considering intereference of top predator in a polluted environment”, Journal of Mathematical Modeling, 3 (2):189-218.
Mishra O.P., Annavarapu R.B. (2016): “A model for the dynamical study of food–chain system considering interference of top predator in a polluted environment”,Journal ofMathematical Modeling, 3(2):189-218.
Mishra O.P., Sinha P., Sikarwar C.S. (2015): “Dynamical study of prey predator system with a commensal species competing with prey species: effect of time lag and alternative food source”, Computational and Applied Mathematics, 34: 343-361.
Ogethakpo A.J., Ojobor S.A. (2021): “ The lotka-volterra predator-prey model with disturbance”, Nigerian Journal of Science and Environment, 19(2): 135-144.
Themairi A. A., Alqudah M.A. (2020): “Predator-prey model of Holling-type II with harvesting and predator in disease”, Italian journal of pure and applied mathematics, 43:744-753.
Wang X., Fan M., Hao L.N. (2017): “Adaptive evolution of body size subject to indirect effect in trophic cascade system”, Biosystems, 159:23–35.
Wang X., Song Le, Jingna L. (2021): “Study on evolution of a predator–prey model in a polluted environment”, Nonlinear Analysis: Modelling and Control, 26(6):1052-1074.
