系统研究了复杂系统的Scale-free问题,包括复杂系统的Scale-free性、幂律分布的分析、Scale-free性的形成机制、复杂系统的Scale-free现象,以及复杂系统Scale-free性的宏观调控等问题。研究结果强调:(1)从广义上说,Scale-free性是描述大量复杂系统整体上严重不均匀分布的一种内在性质;(2)证明了只有当幂律指数在2～3之间时,用幂律分布所描述的大量复杂系统才具有严重的不均匀分布特性;(3)对于国计民生有重大影响的复杂系统,提出了Scale-free性的宏观调控的原则方法。

Scale-free issues of complex systems, including scale-free property of complex systems, analysis of power law distribution, the evolving mechanisms for scale-free property, scale-free phenomena of complex systems, and macro-control of scale-free property, are systemically researched in this paper. We emphasize that: ①Generally speaking, scale-free property is one of the intrinsic characteristics of complex systems, which describes their overall extremely uneven asymmetry distributions; ②Various complex systems with power-law distribution are highly heterogeneous only when their scaling exponents are between 2 and 3, which is proved theoretically by the authors; ③The macro-control principle for the scale-free property of the very important complex systems involved in the national economy and the people's livelihood is proposed.