15 May 2001

Boris Kruglikov "Mathematical models of SOC".

The talk is a short review of a series of papers by Cessac, Blanchard and Krüger on a continuous energy model of self-organized criticality (SOC). We discuss briefly Dhar's model, but concentrate mainly on the one of Zhang. This model has a good dynamical description. The standard trick is to use Bernoulli shifts as a model of random motion (excitations in our case). Given product decomposition of the phase space, the dynamical systems becomes simply-describable. It is hyperbolic and has non-zero Lyapunov exponents. This points rather towards chaos (positive entropy), but in thermodynamic limit the hyperbolicity vanishes and SOC exponents are obtained and observed.