Analyzing atmospheric stability and pollution dispersion through impulsive models

Abstract

This study investigates the stability, uniqueness, and practical applications of a system of impulsive differential equations modeling atmospheric dynamics. The model integrates key atmospheric variables, including pressure, temperature, and wind speed, along with pollutant concentration, to analyze their interactions under periodic impulsive effects. The theoretical framework is developed using the upper and lower solutions method and Lipschitz continuity to guarantee the existence, uniqueness, and asymptotic stability of the solutions. Numerical simulations support the theoretical results, showing how impulsive emissions affect stabilization dynamics. All variables stabilize over time, even when impulse magnitudes vary. The findings demonstrate the robustness of the system and its relevance to air quality modeling, offering insights for policymakers in developing strategies to mitigate pollution and promote environmental sustainability. Future research could extend this work by incorporating stochastic impulses, nonlinear dynamics, and interactions among multiple pollutants to improve model accuracy and predictive capability.