摘要
我们每个人都身处相互联系的网络世界中。比如互联网,电力网,合作网,铁路网,航空网,社会关系网,这些网络的良好运行直接关系到我们的生活和环境。网络信息的同步发送给我们带来信息阻塞,中国南方雪灾对铁路网的破坏使我们出行困难,恐怖主义事件的爆发严重影响人们生活和情绪。所以科学家们一直很关注网络以及网络上的一些现象并努力了解其动力学行为以及背后的运行机制。
现在,网络研究已经渗透到各个科学领域,比如,社会学,生态学,各种自然学科。同时,网络研究也为我们提供了一个巨大的平台,帮助我们更好的应对各种重大社会挑战。为了研究网络上的现象和行为,我们不仅要从宏观上把整个系统作为研究对象,而且需要从微观上来探究每个个体之间的相互作用,通过微观的个体活动以及个体之间相互作用来预言丰富的整体行为并进一步揭示整个系统的宏观现象形成机理。总之,网络分析的观点帮助我们从一个新的高度来理解世界中各系统是如何运作的。
本文的主要研究内容和创新点如下：
(1)在同步能力方面,提出了广义自适应方法,在这种自适应方法中,节点所受到的耦合强度不仅仅根据节点和它的邻居之间的局域同步性质变化,而且受到它’的局域结构特征量—度的调节。我们从数值模拟和理论分析上都证明,广义自适应同步后,网络的输入耦合强度V和度k之间呈现幂律关系：V～k-θ,这里的指数θ为α的函数,他们之间存在关系θ=(1+α)／2。对广义自适应方法,节点的强度可以由α来调节,而且,当α≈1时,网络更加均匀,因此,比原始自适应方法有更好的同步能力。我们发现,网络的同步时间也能在很大程度上缩减。需要强调的是,我们的理论工作不仅仅对真实系统中网络结构和动力学之间的相互作用给出了更深的理解,而且提供了一种通过局域自适应来操控全局集体动力学的方法。
(2)提出了一种具有历史记忆效应的意见动力学模型。考察了这个模型中四个参数对序参量超过某一临界值这一现象发生的时间间隔概率分布的影响。其中,记忆参数和序参数决定了分布曲线的所属类型。环境影响参数和类温参数决定了幂律分布的指数。
(3)通过对经验数据的统计,考察了恐怖主义时间间隔的分布,并且用意见动力学模型解释了实证结果。实证结果表明：真实的恐怖主义爆发的时间间隔概率分布服从幂律形式。我们认为这是个人意见演变的宏观结果。假设在整个恐怖主义演变过程中,个体可以有反对和同意两种态度。当个体与邻居大部分人意见相同时,个体会受环境和记忆的影响,以一定概率改变自己意见。当个体的意见和周围邻居大部分人相反时,个体凭借记忆做出选择,在历史记忆的作用下以一定概率改变自己意见。这里,类温参数是社会混乱程度的一个衡量,环境因素和记忆效应的影响表现为以个体的社会从众性心理和自我认定心理为主的个人心理效应。我们定义了新的序参量来衡量群体反对意见强度,当反对意见强度超过一定极限,也就是序参量小于某个值时,恐怖主义事件爆发。最终,模型结果可以覆盖全部实证结果。我们的假设是正确的。
这些工作已经分别发表于：Phy. Rev. E 81,026201 (2010); Chin. Phys. Lett.27, 068902 (2010).
Each of us is living in the world of connected networks, such as the Internet, power grids, collaboration networks, railway network, air network and social network. The good performance of these networks is directly related to our lives and the environment. Synchronization information sent to us can block the network, snowstorms in the south of China destructed the rail network and made our travel difficult, and the outbreaks of terrorism seriously impacts on people's lives and emotions. Thus scientists have been very concerned about all kinds of networks and the phenomena on networks. They have also been working hard tofind out the dynamic behavior and the underlying Mechanism.
So far, the researches about network have penetrated into all fields of science, for example, sociology, ecology and natural subjects. Meanwhile, the networks also provide us a great platform which help us better deal with some major social challenges. In order to study the phenomena and the behaviors on networks, we should take the entire system as the research object from the macroscopic and should explore the interaction between each individual from the microscopic. We try our best to predict a rich macroscopic phenomenon and to reveal the underlying mechanism by individual activities and the interactions between individuals, In short, the methods of network analysis can help us understand how the system in the world works from a higher level.
The main research content and innovations are as follows:
In the aspect of synchronizability, we proposed the generalized adaptive coupling method where the coupling strength of a node from its neighbors not only develops adaptively according to the local synchronization property between the node and its neighbors (dynamical part) but also is modulated by its local structure, degree of the node. We can show the numerical and analytical results that the input coupling strength of the network after synchronization displays a power-law dependence on the degree, k-θ, where the exponent 6 is controlled by a andθ=(1+a)/2. Compared to the original adaptive coupling method, after the addition of modulation, the distribution of the node's intensity is tunable and can be more homogenous withα≈1, which results in the better synchronizability. It is also found that the synchronization time can shrink greatly. Our theoretical work in the context of synchronization provides not only a deeper understanding of the interaction between structure and dynamics in real world systems, such as opinion formation and concensus, but also potential approaches to manipulate the global collective dynamics through local adaptive control.
We proposed an opinion dynamics model with history memory effect. Investigated the influences of four parameters in this model on probability distribution of the inter-event time where the order parameter exceeds a critical value. Finally, we found the memory parameter and order parameter determine the curve type of the distribution. Environmental impact parameter and the temperature-like parameter decide the exponent of power-law distribution.
The inter-event time of terrorism attack events is investigated by empirical data and the analysis of opinion dynamics model. Empirical evidence shows that the distribution of inter-event time follows a scale-free property. Here we consider the assumption that the burst of a terrorism events is closely relative to the formation of opinions. In the progress of public opinion formation, every individual has his/her own viewpoint, support or opposition. The individual changes his/her own opinion with some probability determined by the circumstance and history memory when the individual has consistent opinion with the majority of his/her adjacent neighbors. However, the individual changes his/her own opinion with some probability according to the history memory in the opposite case. Here the temperature-like parameter is a measure of social chaos, and the environmental factor and the history memory effect represent the individual psychological effects of social conformity and self-affirmation. A new order parameter defined denotes the intensity of the public opposition opinion. The terrorism event outbreaks when the new order parameter is less than a critical value. Ultimately, the model results can cover all the empirical results and our assumption is correct.
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