Damage spreading in the Bak-Sneppen and ballistic deposition models: critical dynamics and nonextensivity. (English) Zbl 1059.37071
Summary: 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.
MSC:
| 37N25 | Dynamical systems in biology |
| 92D15 | Problems related to evolution |
| 37E99 | Low-dimensional dynamical systems |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 82C41 | Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics |
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