A COMPREHENSIVE INVESTIGATION INTO DETERMINISTIC AND STOCHASTIC MODELS CONCERNING THE EFFECTS OF SEEDING ON RAINFALL AND ATMOSPHERIC POLLUTION.

This study introduces a mathematical model aimed at evaluating the potential influence of aerosol introduction into the atmosphere for inducing rainfall and managing atmospheric pollution. By expanding on the proposed model, we incorporate stochastic elements to encompass environmental white noises that impact the system's dynamics. Both mathematical and numerical methods are employed to analyze the system's behavior. In the context of the deterministic model, we examine the solutions' positivity and boundedness, identify feasible equilibria, and scrutinize the stability characteristics both locally and globally. The analysis of the stochastic system encompasses discussions regarding the existence of a unique solution, its ultimate boundedness, and the conditions that prompt the establishment of a unique stationary distribution characterized by ergodic properties. Our simulations illustrate that augmenting cloud formation rates and externally introduced aerosols can amplify rainfall while mitigating atmospheric pollution levels. Minor intensities of white noise do not alter the system's behavior, whereas significant intensities result in high-amplitude oscillations of the system's variables. We explore the effects of white noise intensities using histograms and stationary distributions, highlighting long-term rainfall trends in a noisy environment. [ABSTRACT FROM AUTHOR]