Analysis and Simulation of Evolution Induced Catastrophe

A model of evolution induced catastrophe (EIC) characterized by a nonlocal interaction is proposed. The general feature of the model is its two bias states: explosively catastrophic and globally stable, both consisting in a cascade of locally unstable states. A one-dimensional analysis reveals a transition region from globally stable to catastrophe. A two-dimensional simulation gives a thin fractal fracture profile similar to that observed and also a possible spectrum of fracture fractal. All these are different from percolation. Hence, the EIC model may represent a prototype of natural processes.