Research On Non-markovian Spreading And Growth Process On Complex Networks

Network spreading dynamics mainly focuses on the diffusion of disease,information or substances in the network systems,reveals the essential characteristics of the network propagation process,then provides effective theoretical support for the control of disease in the social networks and the containment of rumors on the Internet.Through long-term development,Markov process in complex network has formed a complete theoretical analysis framework.However,many spreading processes on real networks have non-Markov characteristics,such as the time distribution of human social activities usually shows heavy tail characteristics.Accordingly,it is found that for the spreading process on a network,the heterogeneity of waiting time will hinder the spreading process to some extent.But the Markov process can not analyze the real world spreading process.In contrast,non-Markov process can describe them well.In order to further reveal the influence of non-Markov characteristics on the propagation process,this paper studies the propagation process on complex networks on the basis of predecessors.Compared with the existing methods of network spreading dynamics,the second-order mean field theory get more accurate results.This thesis derives a second-order mean field theory that can accurately predict the outbreak process of non-Markov SI and SIR models in complex networks,and establishes partial differential equations to solve the disease propagation process,which can predict the time evolution process of disease outbreak in the network.In addition,we calculate the average time of each node infected in the network,so as to determine which nodes are more likely to be infected in the process and this has a certain guiding significance for the prevention and control of infectious diseases.Besides,through the experimental simulation on different artificial networks and real networks,we find that the theoretical results are in good agreement with the simulation results,which further verifies the accuracy of the theoretical method.Network spreading dynamics is not only of great significance in epidemic prevention,but also has important application value in other real networks.In this thesis,using the propagation characteristics of SI model,we represent the growth process of clonal plant ramets network on the plane lattice.The experimental simulation results show that in the lattice environment composed of the regular triangle lattice and the square lattice,the ramets network tends to grow longitudinally,which shows the ability to explore the surrounding area better.In the regular hexagon lattice environment,the ramets network tends to grow laterally and has more leaf nodes,which shows the ability of exploit resources in the area,and the number of ramets increases faster.By applying the knowledge of network spreading dynamics to the ecological network,this paper reveals the adaptive characteristics of clonal plant ramets network,which not only embodies the importance of studying the network spreading dynamics model,but also shows the wide applicability of the network science.