Modeling the effect of population pressure on the dynamics of carbon dioxide gas

Abstract

To understand the effect of population pressure (demand of population for forestry trees and land) on the atmospheric level of carbon dioxide gas, a nonlinear model is formulated and analyzed. In formulating the model, four dynamical variables namely; concentration of carbon dioxide, human population, population pressure and forest biomass are considered. In the modeling process, it is assumed that the atmospheric level of carbon dioxide gas increases naturally as well as through anthropogenic emission. Further, it depletes naturally and due to its uptake by the forestry biomass. Moreover, it is assumed that both the human population and forestry biomass follow logistic growth and the population pressure reduces only the carrying capacity of forestry biomass, which decreases the absorption rate of $\hbox {CO}_2$ by forests. Feasibility and stability of equilibria are discussed. Analytical findings demonstrate that as deforestation rate due to human population crosses a critical value, the system destabilizes and oscillations arise through Hopf-bifurcation. Also, it is found that transcritical bifurcation takes place between two equilibria. Our analysis reveals that as the reduction rate coefficient due to population pressure increases, the forestry biomass decreases and the concentration of carbon dioxide increases. Numerical simulation is performed, which supports analytical findings. It is also noted that the dynamics of $\hbox {CO}_2$ is much affected by anthropogenic emissions but the impact of deforestation due to population pressure can not be ignored.