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Models for climate often have many time and length scales which means that the dynamical equations that govern their behaviour can best be described in terms of non-smooth differential equations. These equations have very different behaviour from smooth systems, with very rich dynamics and associated 'discontinuity induced' bifurcations. This rich dynamics impacts on our analysis of the associated climate models. I will illustrate this through two examples. One is the PP04 model for the ice ages with a (possible) explanation of the mid Pleistocene transition via a 'grazing' bifurcation. The other is the Stommel box model for the AMOC circulation. I will show that non-smoothness can lead to a (possible) advancement in the tipping behaviour associated with this system.
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