Modeling the control of atmospheric carbon dioxide through reforestation: effect of time delay

Abstract

Carbon dioxide (CO 2) is the prime greenhouse gas responsible for the threat of global warming. Forest biomass plays an important role in sequestration of carbon dioxide from the atmosphere but the global forest biomass is declining with an alarming rate due to human activities. In this scenario, reforestation is crucial to reduce the atmospheric burden of CO 2. In this paper, we propose a nonlinear mathematical model to study the effect of reforestation as well as the delay involved in between the measurement of forest data and implementation of reforestation efforts on the control of atmospheric concentration of CO 2. Model analysis shows that the atmospheric concentration of CO 2 decreases due to reforestation but a longer delay in between measurement of forest biomass and implementation of reforestation efforts has destabilizing effect on the dynamics of the system. The critical value of this time delay is found analytically. The Hopf-bifurcation analysis is performed by taking time delay as bifurcation parameter. The stability and direction of bifurcating periodic solutions arising through Hopf-bifurcations are also discussed.