Stability Analysis of Fixed Points in Forest Biomass Depletion Model

Abstract

The main focus of this article is to present a model that explains the depletion in forest biomass due to population size , population pressure , and industrialization . This research explores the complex relationship between forest biomass, population growth, and industrialization. The model generates four fixed points that are all non-negative, and they are known as and . The article proceeds to analyze the stability of these fixed points in the context of forest biomass depletion. It is discovered that the fixed points and are saddle points and not stable, while the fixed point is stable if it meets certain conditions. The article concludes by carrying out numerical simulations to determine the equilibrium point of the model, which shows that forest resource biomass stability declines as population size, population pressure, and industrialization increase. The simulations reveal that population growth results in a depletion in forest resource biomass, while the opposite is true for the positive impact that forest resource biomass on population levels. Consequently, it is essential to regulate population density and industrialization to manage population growth and protect forest resources.