复杂动态网络上的传播行为分析 献给清华大学郑大钟教授

Spreading dynamics on complex dynamical networks

随着网络科学的兴起,网络上的传播动力学引起了控制论、博弈论、系统科学、人工智能、社会学、经济学、生物学、心理学、物理学、数学和计算机科学等领域的共同关注.虽然网络上的不同传播行为具有各自的传播规律,但其传播特征总是依赖于网络结构.在实际的复杂网络化系统中,个体间的交互范围不断变化,因此,理解复杂动态网络上的传播行为需要考虑传播动力学与网络演化动力学的耦合.针对当前动态网络上的传播动力学研究主要采用Monte Carlo仿真、缺乏系统理论方法的问题,我们提出随机网络拓扑更新规则,证明该规则为可逆Markov链,并给出其稳态分布,从理论上分析动态网络上的传播动力学.利用该方法,本文以合作演化、疾病传播、疫苗接种为例,给出传播行为分析,揭示动态网络上的演化博弈策略传播行为与疾病传播行为的共性与区别,有望为复杂动态网络上的传播动力学分析提供统一的理论框架.

With the development of network science,spreading dynamics on networks have attracted intensive research interests in a wide variety of areas,such as control theory,game theory,system science,artificial intelligence,social science,economics,biology,psychology,physics,math,and computer science.Network structure plays a key role in spreading dynamics,although spreading dynamics differ from one another.In real networked systems,the neighborhoods of individuals evolve with time.It is thus necessary to consider the coupling between spreading dynamics and network dynamics.Nowadays the research on spreading dynamics on dynamical networks usually use Monte Carlo simulation rather than theoretical methods.So,we propose a stochastic linking dynamic in this paper.It is proved to be a reversible Markov chain,which facilitates the analytical investigation of spreading dynamics on dynamical networks.With this method,we study three spreading dynamics:the evolution of cooperation,the spread of epidemics,and the evolution of vaccination behavior.Furthermore,we show the similarities and differences between evolutionary game dynamics and epidemic spreading dynamics.Our method could provide a universal framework to study spreading dynamics on complex dynamical networks.