M-G-P型复杂网络中有寿命节点的进入退出机制  

The Mechanism of the Entry and Exit of a Node with a Lifetime in a M-G-P Type Complex Network Model

作　　者：马涛[1,2] 郭进利[1] 王福红[1] 王俊芳[1] 徐黎源[2] 钟在明[2] 

机构地区：[1]上海理工大学管理学院,上海200093 [2]嘉兴职业技术学院工商管理教研室,浙江嘉兴314036

出　　处：《数学的实践与认识》2017年第15期285-292,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金项目"超网络及其零行列式策略博弈演化机制研究"(71571119)

摘　　要：现实中复杂网络结构复杂,形式多样,处在高度动态变化的过程.为了更好地理解真实网络的演化,基于复杂网络的特性进行分析,建立了Poissotn连续时间增长节点具有寿命的M-G-P型复杂网络模型,模型中包括:新节点加入、节点老化和老节点退出等,基于齐次马尔可夫链对模型的度分布进行计算,得出M-G-P型网络的度分布符合幂律分布,模型和BA模型一样能产生指数γ=3的无标度网络,验证了导致无标度网络度分布特征起关键性作用的是链接的偏好特性.In reality, complex networks have various forms and complex structures in a highly dynamic and changeful process.In order to better understand the evolution of the real net- work, this paper proposes a M-G-P type complex network model by using a Poissonprocess and a continuous time increase in which the node has the lifetime based on the property of the complex network.The model includes that a new node is added,a node is aging and an old node exits etc.Furthermore,we calculated the degree distribution of the model based on homogeneous Markov chain.It is concluded that the degree distribution of the M-G-P type complex network obeys a power-law degree distribution.The model can produce the same scale-free network with the degree exponent γ= 3 as the BAmodel.The result shows that the preferential attachment plays a key role in the degree distribution feature of the scaie-free network.

关 键 词：复杂网络 马尔可夫链 节点具有寿命 节点进入退出 

分 类 号：O157.5[理学—数学]