Nonlinear dynamics of natural hazards

In this paper we consider the nonlinear dynamics of several natural hazards and related models. We will focus our attention on earthquakes, landslides, and forest fires. These are clearly complex phenomena but they exhibit self organization. A consequence of this self organization is scaling laws. We will consider frequency-magnitude statistics and recurrencetime statistics. The frequency-magnitude distributions are power-law and we give a cascade model of cluster coalescence to explain this behavior. The return-time distributions are well approximated by the Weibull distribution. An important characteristic of the Weibull distribution is that it is the only distribution that has a power-law hazard function.