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Computational Ecology and Software, 2026, 16(1): 35-57
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Article

A dynamical model describing how acid rain affects the growth of plants in a habitat

Niranjan Swaroop1, Ram Naresh Tripathi2, Shyam Sundar3
1Department of Mathematics, Christ Church College, Kanpur-208001, India
2Department of Mathematics, School of Basic and Applied Sciences, Harcourt Butler Technical University, Kanpur-208002, Indiaand
3Department of Mathematics, Pranveer Singh Institute of Technology, Kanpur-209305, India

Received 24 June 2025;Accepted 10 August 2025;Published online 20 August 2025;Published 1 March 2026
IAEES

Abstract
Acid rain formation in the atmosphere is a serious environmental hazard that causes enormous ecological harm. It is formed by the interaction of air pollutants with vapour clouds. It threatens biodiversity, damages ecosystems, and has a negative effect on plant growth. In this paper, we propose a nonlinear mathematical model to examine how acid rain affects the growth of plant biomass in a habitat. The model takes into account five important factors: the density of plant biomass, the density of human population, the cumulative density of sources that release pollutants, the cumulative concentration of pollutants, and the cumulative concentration of acid rain. The model makes the assumptions of logistic growth for both human population density and plant biomass, which is adversely affected by acid rain. The model analysis shows that increasing the concentration of acid rain leads in a considerable drop in plant biomass density. The model analysis, which employs the stability theory of differential equations, shows that a substantial decrease in plant biomass density at equilibrium results from rising acid rain concentrations or human population density. These findings are supported by numerical simulations, which show that acid rain has a considerable effect on plant biomass growth. This study provides a framework for understanding the ecological consequences of acid rain.

Keywords mathematical model;stability;plant biomass;population density;acid rain.


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