Recent empirical studies have witnessed the wide existence of double power-law distribution in complex systems. However its underlying origin remains inadequately disclosed. We show this distribution can arise from the proper control of BA model. Particularly, the control policy demands each new edge to determine the range(degree$\le k_c$ or $>k_c$) of its target node by probability $p$ before applying the preferential attachment. We analytically derive the degree distribution and demonstrate a critical control parameter $p_c$ so that normal and reversed double power-law degree distribution emerges for $p>p_c$ and $p<p_c$ respectively, and a single power law is recovered when $p=p_c$. The control policy of our model can spontaneously result from various constraints, which provides possible explanation for some real systems and indicates the validity of our model.

最近的实证研究已经看到在复杂系统中广泛存在双重幂律分布。但是，其潜在来源仍未充分公开。我们证明了这种分布可能源于对BA模型的正确控制。特别地，控制策略要求每个新的边缘来确定范围（度$\le {ķ}_C$ 要么 $>{ķ}_C$目标节点）的概率 $p$在应用优先附件之前。我们通过分析得出度分布并演示关键控制参数$p_C$ 因此出现了正态和逆向双幂律度分布 $p>p_C$ 和 $p<p_C$ 分别，并且当 $p=p_C$。我们的模型的控制策略可以自发地受到各种约束的影响，这为某些实际系统提供了可能的解释，并表明了我们模型的有效性。