A mean-field Bak-Sneppen model with varying interaction strength

We propose a mean-field Bak-Sneppen (MFBS) model with varying interaction strength. The interaction strength, here denoted by alpha, specifies the degree of interaction, and varies smoothly between 0 for no interaction and 1 for full interaction (restoring the original BS model). Our simulations of the MFBS model reveal some interesting features. When beta is non-zero, the MFBS model can evolve to a self-organized critical (SOC) state. The critical exponent of the avalanche size distribution, tau, is insensitive to changes in alpha. The critical exponent of average avalanche size, gamma, and the avalanche dimension exponent, D, both increase slightly with alpha < 0.5 but remain constant if alpha > 0.5. The critical threshold f (c) decreases almost linearly with alpha.