The Dynamics Research Of Collective Behaviors On Networks

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.