中文摘要：

本文对K-K择优增长系统作出进一步的研究,提出一类既有择优增长、又有随机增长的混合增长系统,利用马氏链方法严格证明了系统度分布的存在性,并给出其精确解。结论表明只要系统中存在择优增长,该系统即为无标度系统,且系统的度指数随着择优增长所占比重不同而变化.

英文摘要：

We study a class of preferential growth system （K-K model） and promote the model to a both preferential and random growth system. 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. The conclusion shows that as long as the preferential growth existed in the system, the system has scale-free property, and the index of degree distribution changes in accordance with the proportion for preferential growth to both preferential and random growth of the system.