A mathematical model to study the dynamics of carbon dioxide gas in the atmosphere

A nonlinear mathematical model to explore the effects of human population and forest biomass on the dynamics of atmospheric carbon dioxide (CO2CO2) gas has been proposed and analyzed. In the modeling process, it is assumed that the concentration of CO2CO2 in the atmosphere increases due to natural as well as anthropogenic factors. Further, it is assumed that the atmospheric CO2CO2 is absorbed by forest biomass and other natural sinks. Equilibria of the model have been obtained and their stability discussed. The model analysis reveals that human population declines with an increase in anthropogenic CO2CO2 emissions into the atmosphere. Further, it is found that the depletion of forest biomass due to human population (deforestation) leads to increase in the atmospheric concentration of CO2CO2. It is also found that deforestation rate coefficient has destabilizing effect on the dynamics of the system and if it exceeds a threshold value, the system loses its stability and periodic solutions may arise through Hopf-bifurcation. The stability and direction of these bifurcating periodic solutions are analyzed by using center manifold theory. Numerical simulation is performed to support theoretical results.

► A mathematical model to explore the dynamics of atmospheric CO2 has been proposed.
► Deforestation rate has destabilizing effect on the dynamics of the system.
► Hopf-bifurcation analysis is performed by taking deforestation rate coefficient as bifurcating parameter.
► Stability and direction of the bifurcating periodic solutions are analyzed.
► Prevention and control of deforestation is a potential strategy for the stabilization of future CO2 concentrations.