Damage spreading in the Bak–Sneppen and ballistic deposition models: critical dynamics and nonextensivity

We introduce a new damage spreading algorithm which is able to capture both the long-time and short-time dynamics of extended systems which evolves towards a critical statistically stationary state. In this sense, the dynamics of systems exhibiting self-organized critical states is shown to be similar to the one observed at the usual critical point of continuous phase transitions and at the onset of chaos of nonlinear low-dimensional dynamical maps. The proposed algorithm is applied to the Bak–Sneppen model of biological evolution and the ballistic deposition model of surface growth. The critical dynamics of these models are discussed within the framework of a nonextensive statistics formalism.