【作者】 林颖婷；

【导师】 汪秉宏；

【作者基本信息】 中国科学技术大学 ， 理论物理， 2014， 博士

【摘要】 复杂网络上的动力学研究通常具有现实背景,对理解、控制、优化真实系统有着深刻的现实意义。相比其他由客观体所组成的复杂系统,由人组成的社会系统包含着更复杂的动力学机制。本文采用基于agent的仿真建模方法,研究了社会网络上的意见动力学和人类创新行为动力学。(一)我们提出了一个意见动力学模型,研究了节点异质影响力对系统收敛时间的影响。我们根据节点度的大小,赋予节点代表影响力的权重,又引进了一个可调α对该权重进行进一步调节。研究发现,系统中存在一个最优值a,使系统的收敛时间最短。这个结论对无标度网络、ER随机网络、小世界网络都成立。为解释这一现象,我们观察了节点初始意见成为最后舆论共识的概率与节点度的关系、意见团簇数目的演化过程,并发现适中的α平衡了团簇内部凝聚力和团簇间的竞争力,使系统收敛最快。另外我们发现,收敛时间随网络规模变化的曲线为幂函数,幂指数的大小取决于α。此项工作有利于我们理解个体属性的异质性对意见动力学演化的作用。(二)如何促进创新活动是现代社会的一个重要问题。我们结合演化博弈和信息传播过程,提出了一个收益驱动的人类创新行为动力学的最简模型。我们考虑的是广义上的人类创新行为(innovative behavior),指一切原创并会带来其他跟随者参与的行为。我们根据日常中人们对创新行为的直观感受,做出以下假设：个体可选创新Ⅰ或跟随F作为信息更新策略；成果扩散范围越大,给个体带来的奖励越丰厚；创新比跟随要需要付出更高的代价；个体学习成功者的策略。我们发现创新代价α是影响创新系统动力学演化的关键因素。系统动力学演化呈现出准局域化的特点,出现了创新者聚集的创新中心,创新策略长时期徘徊在小区域内,扩散缓慢。这些现象符合我们对人类创新行为的日常认知。此外,我们的模型还出现了丰富的非泊松时空统计特性：采纳创新策略的时间间隔分布呈幂律分布、连续持有创新策略的时长分布呈幂律分布、创新成果传播范围分布呈带幂律的双峰分布。我们的模型提供了一个研究人类创新行为演化的基本框架,对促进创新活动提供了有益的建议。(三)在上述的研究成果的基础上,我们在BA网络上,研究了异质网络上创新行为的演化过程。我们发现,创新活动的相对代价α依然显著影响着创新行为的动力学演化,减少创新代价依旧是促进创新活动的有效方式。创新者和跟随者、创新者和创新者之间都是相互竞争又相互依存的关系带来了异于其他演化博弈模型的行为模式：较高的网络平均度(k>在α较低的情况下促进了创新,但同时也降低了系统对高代价α的承受能力。系统呈现了丰富的非泊松时空特性,准局域化的图景依然存在。同时,节点度不同的个体在动力学行为上呈现出了异质性,具有不同的策略选择倾向。更多还原

【Abstract】 Dynamics research on complex networks usually has a realistic background, and is of profound practical significance in understanding, controlling, and optimizing the real system. Compared to other complex system, the dynamics mechanism of social system formed by human beings is much more complex. In present paper, the opinion dynamics and the dynamics of human innovation behavior on social network by agent-based method is studied.(1)We propose an opinion dynamics model to study the effects of heterogeneous influence of individuals on the global consensus. Each individual is assigned a weight of influence according to its degree. A tunable parameter a is introduced to govern the weight of influence. Interestingly, it is found that there exists an optimal value of α, resulting in the shortest consensus time for scale-free networks, ER random networks and small-world networks. To explain this phenomenon, we study the probability of an individual’s initial opinion the same as the final opinion as a function of degree, the evolution of the number of opinion clusters, and find that the medium α balance the cohesion inside the cluster and the competition between clusters, leading to fastest convergence speed. Furthermore, the relationship between average consensus time and the network size obeys the power function controlled by a. Our results are helpful for understanding the role of heterogeneous of individual property in the opinion dynamics.(2) How to promote the innovative activities is an important problem for modern society, In this paper, combining the evolutionary games with information spreading, we propose a lattice model to investigate dynamics of human innovative behaviors based on benefit-driven assumption. We consider the human innovative behaviors in the broad term, which is the behaviors original and followed by more participants. Simulations show several properties in agreement with peoples’ daily cognition on innovative behaviors, such as slow diffusion of innovative behaviors, gathering of innovative strategy on "innovative centers", and quasi-localized dynamics. Furthermore, our model also emerges rich non-Poisson properties in the temporal-spacial patterns of the innovative status, including the scaling law in the interval time of innovation releases and the bimodal distributions on the spreading range of innovations, which would be universal in human innovative behaviors. Our model provides a basic framework on the study of the issues relevant to the evolution of human innovative behaviors and the promotion measurement of innovative activities.(3)Based on the above results, we apply the BA network on the dynamics to study the evolution of innovative behavior on heterogeneous networks. We found that the relative costs a of innovation activities strongly influence on the innovative behavior’s evolution. The relationship between innovators and the relationship between innovators and followers are partly competition and partly dependent, leading to special properties different from other evolutionary games:large average degree (k) of the network can promote the level of innovative behavior, but also reduces the system affordability of cost α. The quasi-localized dynamics still exist and the system emerges rich non-Poisson properties in the temporal-spacial patterns of the innovative status. Furthermore, the individuals with different degrees behave heterogeneously with different strategic choice tendencies.更多还原