Complexity theory of natural disasters ; Boundaries of self-structured domains

Disasters are often represented as complete breakdowns of quasi-stationary states in a landscape, but may also be part of the normal evolution of such states. A landscape is, in fact, an open, nonlinear, dynamic system where the tectonic uplift and the seismic activity represent the input, the mass wastage and the relief degradation the output. The apparent 'stability' is due to the fact that open, nonlinear dynamic systems tend to develop into relatively stable, self-organized ordered states 'at the edge of chaos', with a fractal attractor. Short of complete breakdown, such systems re-establish order in steps of various magnitudes which have a power-law distribution. Because of the fractal structure of the basic attractor, all subsets follow a power law which accounts for the distribution of the steps of recovery. As the domains of quasi-stationarity at the edge of chaos are represented by finite windows, the power-law does not cover all magnitudes. The stationarity windows are not only limited in range, but also in space and time. This should be taken into account in the assessment of hazards. Examples are given from seismology (earthquake frequency), volcanology (eruption frequency), river hydrology (flood frequency) and geomorphology (landslides).