Research On Critical Avalanche Dynamics On Complex Networks

Complex network is the abstraction of complex system,which can describe many real networks like cooperation network,traffic network,power network through nodes and links.In the research of complex networks,scientists not only concerned about the function and evolution of network structures,but also want to understand the spreading dynamical process on complex networks,such as disease spreading and information transmission.Similar to the avalanche phenomenon in nature,some spreading dynamical process can become extremely popular in a short time,which may have a great impact on the life and work of people,while others can only spread in a small range and gradually annihilate.Based on the topology of complex networks,the analysis and research on avalanche dynamics will help people to understand the process and mechanism of the spreading dynamical process,and further provide factual and theoretical suggestions for the early warning and control.Our study focuses on the critical avalanche dynamic on complex network and carries out the following three researches:Firstly,we study the avalanche temporal profile of the epidemic outbreaks for the classical SIR model.At the critical point,the rescaled average terminating and nonterminating avalanche shapes for different durations collapse onto two universal curves respectively,while the average number of subsequent events essentially remains constant.We then propose two numerical measures to determine the epidemic thresholds by analyzing the convergence of the rescaled average non-terminating avalanche shapes for varying durations and the stability of the average number of subsequent events,respectively.Extensive numerical simulations demonstrate that our methods can accurately identify the numerical threshold for the SIR dynamic on both synthetic and empirical networks.Compared with traditional numerical measures,our approaches are transient measures that determine the system state without the final outbreak size,and thus have the advantage of low computational complexity and high prediction accuracy.Then,we collect the information transmission data on the real social network,and reconstruct the diffusion network based on the twitter data.We find that the spreading ability of false information is significantly stronger than that of true information,mainly reflected in the strong heterogeneity of the diffusion network size and depth.Furthermore,we analyze the difference between true and false information on the annual generation and transmission,and find that the annual generation and transmission of false information are significantly more than that of true information,which means that the generation probability and the transmission probability may be two important factors to determine information transmission ability.These findings are greatly significance to the modeling of true and false information disseminationFinally,considering the propagation characteristics of true and false information,we propose a competition propagation model of multiple true and false information,which takes into account both the probability of information generation and transmission.In the case of limited attention of users,different true and false information will compete for users' attention and ultimately lead to the size of a majority of information are very small while the size of a minority of information are extremely large.Extensive numerical simulations demonstrate that the competition of true and false information will transit form insufficient competition state to sufficient competition state,which will lead to the information transmission system change from subcritical state to critical state.Furthermore,we study the impact of information generation probability and transmission probability on the spreading ability and find that they can significantly affect the distribution of information popularity,which is consistent with the empirical data.