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 (CO"2) gas has been proposed and analyzed. In the modeling process, it is assumed that the concentration of CO"2 in the atmosphere increases due to natural as well as anthropogenic factors. Further, it is assumed that the atmospheric CO"2 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 CO"2 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 CO"2. 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.

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