Spreading Dynamics On Multiplex Networks

Up to now,complex network is a young discipline compared with other traditional disciplines,however because of its wide application,it has rapidly become one of the most popular interdisciplines,not only attracted the attention of the mathematician and physicist,but also made the researchers of engineering,computer,biology,finance and other fields pay attention to it at the same time.In daily life,there are a lot of communication process,such as the spread of the disease,emotional transimission,computer virus propagation,diffusion of social behavior etc,these can be referred to as the spread dynamics.Regardless of the discipline development and practical application,the transmission mechanism of the research object need to be explored.Spreading dynamics has become an important branch of complex networks,and many researchers have achieved fruitful results in this branch in recent decades.At first,the researchers pay attention to the spreading dynamics on the singlelayer network,and proposed some classical dynamic models,such as SIS,SIR models commonly used to describe epidemic spread,and threshold models for describing social behavior propagation.In general,the researchers use the knowledge of statistical physics to study the parameters such as the range of propagation or the threshold of propagation.For example,under the thermodynamic limit,the propagation threshold of SIS and SIR models will tend to be zero on heterogeneous networks.In this scale-free network,even if the epidemic spread rate is very small,epidemics are easy to spread in the crowd.However,due to the complexity of the real system,for example,in social network,besides the daily direct contact,we will also use other communication tools to contact each other,such as WeChat,twitter,Facebook and so on.The characteristics of multiple types of connections among the same groups cannot be described by single layer networks,so researchers have proposed using multiple network models to study this problem.In recent years,the research on the spreading dynamics of multiple networks has achieved remarkable results.For example,some researchers use the knowledge of multiple networks to study the impact of message diffusion on the epidemic spreading process,and find that the disease transmission threshold is affected by the message transmission rate.We are inspired by this work.Considering that the transmission of social behavior is often accompanied by the spread of related messages,people in the group take different attitudes to social behavior according to whether they know the news or not.Carbonated soft drinks,for example,in daily life because of its refreshing mouthfeel is popular with people,especially teenagers,but when people know drinking carbonated drinks may be harmful to the body,this part of the population will be more rational than those who did not get a message to buy carbonated drinks.Because it is a widespread phenomenon that the spread of social behavior is accompanied by news diffusion in daily life,it is urgent for us to study how they affect people’s communication and the impact of news diffusion on them.Based on the considerations above,in this paper,we study the spreading dynamics of social behaviors and focus on heterogenous responses of individuals before and after they realize the spreading of the social dynamics.We model the system with two-layer multiplex networks,in which one layer describes the spreading of the social dynamics and the other layer describes the diffusion of the awareness of the dynamics.Moreover,we consider that for an individual if it is unaware of the spreading of social behavior its dynamics will follow SIS model,while when it is aware of the spreading of social behavior its dynamics will follow threshold model.We found that such different reactions stemmed from the awareness and unawareness of the spreading dynamics could induce intriguing dynamical properties.The dynamics of the whole network may exhibit hybrid phase transition with the coexistence of continuous phase transition and bi-stable states.Detailed study of how the diffusion of the awareness influences the spreading dynamics of social behavior is provided.The results are supported by theoretical analysis.We hope it can help to explain the microcosmic mechanism of social behavior propagation under the influence of news diffusion in daily life.