Dynamics of a Nonsmooth Conceptual Climate Model

There is evidence that hundreds of millions of years ago the Earth was largely glaciated, and maybe even completely ice-covered.  We develop a slow-fast conceptual climate model that allows for both of these possibilities and consists of equations for temperature, sea ice, and greenhouse gasses.  The system is naturally nonsmooth and does not fit into any existing analytical framework.  With this in mind, we will explore possible ways to extend the model so that nonsmooth dynamical systems theory can be applied, and will study the implications of our choices.  If time allows, we will look more closely at the "switching manifold" and the nonsmooth canard behavior that can occur.