Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2001-11-13
Nonlinearity 16, 25 (2003)
Nonlinear Sciences
Adaptation and Self-Organizing Systems
14 pages, 3 figures
Scientific paper
10.1088/0951-7715/16/1/302
We introduce the standard distribution width of fitness to characterize the global and individual features of a ecosystem in the Bak-Sneppen evolution model. Through tracking this quantity in evolution, a different hierarchy of avalanche dynamics, $w_{0}$ avalanche is observed. The corresponding gap equation and the self-organized threshold $w_{c}$ are obtained. The critical exponents $\tau ,$ $\gamma $and $\rho $, which describe the behavior of the avalanche size distribution, the average avalanche size and the relaxation to attractor, respectively, are calculated with numerical simulation. The exact master equation and $\gamma $ equation are derived. And the scaling relations are established among the critical exponents of this new avalanche.
Gao Kelin
Lee Chaohong
Zhu Xiwen
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