Avalanche dynamics in Bak-Sneppen evolution model observed with standard distribution width of fitness

Abstract

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.