Coevolutionary dynamics on scale-free networks

TL;DR

This paper studies Bak-Sneppen coevolution models on scale-free networks, revealing how the critical fitness value and avalanche size distributions depend on the degree exponent, with analytical and numerical insights.

Contribution

It provides analytical and numerical analysis of coevolution dynamics on scale-free networks, highlighting the impact of degree exponent on critical fitness and avalanche behavior.

Findings

For γ > 3, critical fitness approaches a nonzero value as network size grows.

For 2 < γ ≤ 3, critical fitness approaches zero.

Avalanche size distribution exhibits different power-law regimes depending on γ.

Abstract

We investigate Bak-Sneppen coevolution models on scale-free networks with various degree exponents $\gamma$ including random networks. For $\gamma >3$, the critical fitness value $f_c$ approaches to a nonzero finite value in the limit $N \to \infty$, whereas $f_c$ approaches to zero as $2<\gamma \le 3$. These results are explained by showing analytically $f_c(N) \simeq A/<(k+1)^2>_N$ on the networks with size $N$. The avalanche size distribution $P(s)$ shows the normal power-law behavior for $\gamma >3$. In contrast, $P(s)$ for $2 <\gamma \le 3$ has two power-law regimes. One is a short regime for small $s$ with a large exponent $\tau_1$ and the other is a long regime for large $s$ with a small exponent $\tau_2$ ($\tau_1 > \tau_2$). The origin of the two power-regimes is explained by the dynamics on an artificially-made star-linked network.