Modeling Vegetation-Erosion Dynamics using Differential Equations with Human Factors

Abstract

The effects of soil erosion are often devastating. Plants can reduce erosion by slowing runoff and reinforcing soil using its roots. In this project, we investigate the dynamic relationship between vegetation and erosion processes. We assume an inverse relationship between vegetation density and soil erosion: that is, an increase in vegetation cover reverses soil degradation and a decrease in vegetation cover intensifies the problem of erosion. We also assume that human activities (like logging, road-building) affect both vegetation development and resilience against erosion. Our model for the vegetation-erosion dynamics is a two-dimensional nonlinear system of differential equations with logistic growth on both variables. Equilibrium and nullcline analysis methods are applied to determine all possible dynamic scenarios between vegetation and erosion. The resulting parameter conditions can be used to analyze bifurcations on the vegetation and erosion dynamics