Modeling the effect of time delay in implementation of mitigation policies on the control of atmospheric greenhouse gases

Mitigation of the enhanced greenhouse gas (GHG) concentrations in the Earth's atmosphere is imperative to meet the climate change mitigation objective. Governments of many countries are developing and implementing various mitigation strategies to reduce their GHG emissions. However, a time delay between the formulation and implementation of these mitigation policies can affect their effectiveness in controlling greenhouse gas levels in the atmosphere. This work presents a nonlinear mathematical model to investigate the effect of application of mitigation strategies and the delay involved in their implementation over the reduction of atmospheric greenhouse gases. In model formulation, it is assumed that the mitigation strategies work two-fold; first they reduce the GHG emission rate from the anthropogenic source and second they increase the removal rate of greenhouse gas from the atmosphere. A comprehensive stability analysis of the proposed model system is made to examine its long-term behavior. The model analysis shows that an increase in the implementation rate of mitigation strategies and their efficiencies to cut down the GHG emission rate from point sources and increase the GHG uptake rate lead to reduction in equilibrium GHG concentration. It is found that a long delay in the execution of mitigation policies can destabilize the system dynamics and leads to the generation of periodic oscillations. The expression for the threshold value of the delay parameter at which periodic oscillations arise via Hopf-bifurcation is determined. The stability and direction of bifurcating periodic solutions are discussed. A sensitivity analysis is performed to investigate the effect of changes in key parameters over system dynamics.