  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.
