【作者】 林海；

【导师】 吴晨旭； 陈丽璇；

【作者基本信息】 厦门大学 ， 理论物理， 2007， 博士

【摘要】 现实生活中大量自然和人工的系统都可以用复杂网络来表征。自从发现大多数实际网络的拓扑结构都具有小世界效应和无标度特性之后,复杂网络已经吸引了越来越多物理学家的兴趣。研究复杂网络的一个主要目的是了解拓扑结构对发生在网络中的动力学过程的影响。信息或物质的传输是网络的一个基本功能,研究其动力学过程对于现代社会具有重要意义。我们构建了一个简单的模型研究大量粒子在具有有限节点容量的复杂网络中同时沿最短路径行走时的拥塞动力学过程。结果表明,当网络中的粒子密度达到某个临界值时,系统将经历从自由流状态到全局拥塞状态的跳变,从而导致网络的全局交通瘫痪。引发网络拥塞的临界粒子密度与网络的拓扑结构有很大的关系。不同拓扑结构的网络其拥塞过程的动力学图像也不同,无标度网络中的拥塞是许多拥堵小团簇的逾渗过程,而其它几种均匀网络中拥塞集团的形成则是类似于晶体结晶的成核生长过程。生物个体间的合作行为如何通过自然选择进化出来是自达尔文以来进化生物学研究的一个基本问题。进化博弈论为理解合作行为的演化提供了一个统一的框架。本文研究了基于遗传算法的重复囚徒困境博弈和鹰鸽博弈策略在复杂网络中的演化。我们假设个体位于复杂网络中,只和自己的邻居进行博弈。这些个体具有历史记忆能力,能够根据自身的基因型及以前的博弈历史采取不同的博弈策略。研究结果表明,这样的个体在复杂网络中经过基因的复制、重组、变异和选择之后,能够自然地进化出一种自组织的合作机制,这种合作机制既能促进合作行为的涌现,加强和维护持续的合作行为,又能对自私的背叛个体进行惩罚和报复。因此有记忆能力的群体能够在复杂网络中进化出很高的合作率。更多还原

【Abstract】 Many natural and artificial systems in the real world can be described by complex network. Since most of the network topological structures were found to show a small-world and a scale-free feature, complex networks have attracted growing interest among the physics community. A major goal of investigation is to unveil how the topological structures of networks influences the dynamical processes on them.For modern society, it is of great importance to study the dynamical processes of the transportation of information or matter on networks, which is one of the basic functions of networks. We constructed a simple model to study the congestion dynamic triggered by multiple particles walking along the shortest path on complex networks which composed of nodes that have a finite capacity. It is found that a transition from free-flow phase to congestion phase occurs at a critical particle density, which varies for complex networks with different topological structures. The dynamic pictures of congestion for networks with different topological structures show that congestion on scale-free networks is a percolation process of many small congestion clusters, while the dynamic of congestion transition on other three homogenous networks is mainly a process of nucleation in analogy to crystal growth.To explain the emergence of cooperation by natural selection has been a fundamental topic of evolutionary biology since Darwin. Evolutionary game theory provides a uniform frame to study the evolution of cooperation. We investigate the evolution of strategies in the iterated prisoner’s Dilemma game and hawk-dove game on complex networks on the basis of genetic algorithm, and the assumption that individuals on complex networks only play games with their neighbors. These individuals have historical memory to update their strategies based on their genotype and the knowledge of past game record. It is found that the individuals can naturally develop some self-organization mechanics of cooperation by genome reproduction, recombination, mutation and selection, which can not only result in the emergence of cooperation, but also strengthen and sustain the persistent cooperation. At the same time, such mechanics punishes and revenges defective individuals, leading to a high cooperation frequency on complex networks.更多还原