中文摘要：

研究文献[1]中提出的一类择优增长系统,将模型推广至成员成批到达的情形,经每时间步,系统中分别增加一个团体和m个成员.这m个成员相互独立的依概率p加入旧团体,且加入旧团体的概率与旧团体中的成员数成正比;依概率q=1-p加入新团体.该文利用马氏链方法严格证明系统度分布的存在性,并给出其精确解,从而得出该系统为无标度系统.

英文摘要：

We study a class of preferential growth system [1] and promote the model to a general situation.Considering there are m elements added to the system at each time step,The m elements can either join in the new group （with probability q =1-p） or dependently join in an already existing group with a probability proportional to the size thereof.Based on the Markov chain theory,we get the rigorous proof for the existence of the steady-state degree distribution and obtain the exact solution,then prove the model has scale-free property.