Title: A study on the dynamical system of the effect of carbon dioxide gas in the atmosphere

Abstract

This paper formulates and analyzes a deterministic nonlinear model to explore the effects of human population and forest biomass on the dynamics of atmospheric carbon dioxide (CO2) gas. The model system tends to assume the concentration of CO2 in the atmosphere increases for the deterministic natural sources along with the anthropogenic factors. Further, the paper has the anticipation on that the density of atmospheric CO2 that forest biomass and other natural sinks absorb. However; the analysis is carried out in continuous time. Equilibria of the model has been obtained and their stability discussed. The model analysis reveals that human density declines with an increase in anthropogenic CO2 emissions into the atmosphere. Further, the findings posit that the depletion of forest biomass due to human activities, deforestation, leads to increase in the atmospheric concentration of CO2. Moreover; this research work purposefully determines bounds for the gas volume and discusses the complexity and stability of the equilibria. Eventually, it culminates to the evidence that the deforestation rate coefficient destabilizes effect on the dynamics of the system and the system loses its stability when the threshold value exceeds. Again; periodic solutions may arise through Hopf-bifurcation. The stability and direction of these bifurcating periodic solutions are analyzed by using center manifold theory. And the demonstration of the numerical simulations helps to support the analytical results.