Analysis Of Several Novel Dynamics Models On Scale-free Networks

In recent years,the research of complex networks has attracted the interest of many researchers,and has penetrated into many different fields,such as mathematical science,life science and engineering science.The emergence of scale-free network model indicates that the study of complex networks has entered a new era.Considering that scale-free network can reflect the social network in the real world more vividly,several new propagation dynamics models based on scale-free networks are established in this paper,and the proposed models are studied and analyzed in detail.The conclusion is in very agreement with the real-life phenomenon.The main work and innovation of this paper include the following aspects:1.To investigate the influence of heterogeneity of the underlying networks and the preferential degree on the spreading of e-commerce preferential information,a novel SIB?Susceptible-Infected-Beneficial?model on scale-free networks is presented.Through mathematical analysis,the basic reproductive number ₀R and equilibriums are obtained in detail.Theoretical results indicate that the basic reproductive number is significantly dependent on the topology of the underlying networks and the preferential degree.The global stability of information-elimination equilibrium is proved.The permanence of preferential information and the global attractivity of information-prevailing equilibrium are studied in detail.2.Considering the influence of demographics and the people's hesitation,a novel SEIR?Susceptible-Exposed-Infected-Removed?rumor spreading model with demographics on scale-free networks is proposed and analyzed in detail.Then,the basic reproductive numberR₀ and equilibriums are obtained.The theoretical analysis indicates that the basic reproduction number has no correlation with the degree-dependent immigration.We prove the globally asymptotically stable of the rumor-free equilibrium.The permanence of the rumor and the global attractivity of rumor-prevailing equilibrium are also studied in detail.Furthermore,we present some effective ways to control the rumor spreading.3.Taking into account the influence of the virus's drug-resistant variation,a novel SIVRS?Susceptible-Infected-Variation-Recovered-Susceptible?epidemic spreading model with variation group on scale-free networks is proposed and analyzed in detail.Then,the basic reproductive numberR₀ and equilibriums are obtained.The relationships between the basic reproductive number,the variation characteristic and the topology of the underlying networks are studied in detail.We analyses the globally asymptotically stable of the disease-free equilibrium.The permanence of the epidemic and the global attractivity of endemic equilibrium are also studied in detail.Furthermore,we present some effective ways to control the epidemic spreading.