An energy balance model of carbon's effect on climate change

Due to climate change, the interest of studying our climatic system using mathematical modeling has become tremendous in recent years. One well-known model is Budyko’s system, which represents the coupled evolution of two variables, the ice-line and the average earth surface temperature. The system depends on natural parameters, such as the earth albedo, and the amount A of carbon in the atmosphere. We introduce a 3-dimensional extension of this model in which we regard A as the third coupled variable of the system. We analyze the phase space and dependence on parameters, looking for Hopf bifurcations and the birth of cycling behavior. We interpret the cycles as climatic oscillations triggered by the sensitivity in our regulation of carbon emissions at extreme temperatures.