Stochastic Differential Equations in Population Dynamics: Modeling and Analysis

Abstract

This study explores the application of stochastic differential equations (SDEs) in modeling population dynamics. By introducing randomness into differential equations, we capture the inherent uncertainties in environmental and genetic factors affecting population growth. We derive analytical solutions for specific cases and provide numerical simulations to demonstrate how SDEs enhance predictions in ecological modeling. Our findings suggest that stochastic models provide a more robust framework for understanding population fluctuations in uncertain environments.