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In this paper we analyse a dynamical system based on the so-called KCG(K\"all\'en, Crafoord, Ghil) conceptual climate model. This model describes anevolution of the globally averaged temperature and the average extent of theice sheets. In the nondimensional form the model is prone to severalsimplifications facilitating the subsequent analysis. We consider the limitingcase of the stationary snow line for which the phase plane can be completelyanalysed and the type of each stationary point can be determined. One of themcan exhibit the Hopf bifurcation for which occurrence we find the sufficientconditions. Those, in turn, have a straightforward physical meaning andindicate that the model predicts internal oscillations of the climate. Usingthe typical values of model parameters we conclude that the obtained resultsare in the same ballpark as the conditions on our planet during the quaternaryice ages. Our analysis is a rigorous justification of a generalization of someprevious results by KCG and other authors.

Hopf bifurcation in a conceptual climate model with ice-albedo and precipitation-temperature feedbacks