The Study Of Threshold Model Based On Gillespie Algorithm

With the rapid development of information technology,ways of communication are more and more diversified,and the channels of information dissemination are more and more extensive,which has created complex systems that are increasingly complex in life.Complex networks are an effective means to study real complex systems,abstracting real individual or system subsets into nodes in the network,and using the connected edges between nodes to represent a particular connection between individuals.The real complex system is abstracted into a simple network structure in this way.This approach makes complex networks popular in various fields,and it also raises the study of propagation dynamics on complex networks.Research on the structure of the network helps us understand the real complex systems and the various propagation phenomena in the system.The process such as the adoption of commercial products,the spread of rumors,and the diffusion of opinions are ubiquitous in the social system.They can be all described as contagion processes,in which a thing like information or idea passes from one person to another through the association between the two individuals,analogous to the infection of diseases.This kind of contagion process is of particular interest in sparsely connected networks,in which the topology of the network has a big impact on the outcome of the spreading process,giving rise to a set of interesting phenomena.The models to study these processes generally fall into the two categories: simple contagion and complex contagion.The simple contagion is motivated from disease spreading,which models the spreading process as infectious disease passed from one to another through independent interactions.The complex contagion is inspired from collective behaviors in social systems.It assumes that the infection will occur only when some critical mass have reached,The critical mass usually refers to the proportion of individuals who receive this information.Through the distinction between these two different propagation mechanisms,the models in complex networks are generally divided into two types: independent interaction models and threshold models.The common infectious disease model in the network-SI,SIS model,and independent cascade model belong to the independent interaction model.The characteristics of this type of model are that the contact between individuals is independent of each other,and as the effective contact between individual increases,the probability of an individual being infected increases.Threshold model means that certain conditions must be met before propagation occurs.Common methods for simulating propagation models include discrete-time simulation methods and continuous-time simulation methods.Most of the current researches on propagation models are usually based on discrete-time simulation methods.There are few propagation models based on continuous-time simulation methods,and discrete-time approximation methods are commonly used to achieve continuous-time simulation.At present,researchers have studied the difference between the discrete time approximation simulation method and other continuous time simulation methods,and found that the discrete time approximation method has many limitations compared with the continuous time simulation method.The discrete time approximation method has a certain limit on the time.If the time intervals are too large,the obtained propagation dynamics process will be inaccurate.So far,the research on threshold model is mostly based on discrete time simulation method,lacks the study of simulating threshold model with continuous time.This paper proposes to apply the Gillespie algorithm to the threshold model to construct a continuous time threshold model.When the Gillespie algorithm constructs a continuous time threshold model,it can clearly determine when the next random event occurs and the next random event.This advantage of Gillespie algorithm greatly simplifies the numerous calculations in the discrete time simulation method and improves the efficiency of the algorithm.By constructing a continuous time threshold model,we compare it with the linear threshold model and analyze the two shortcomings of the linear threshold model.Based on the simulation of the continuous threshold model,the continuous time threshold model can be compared with the continuous time SI model on the same level,and the macroscopic comparison of the two propagation models with different microscopic propagation mechanisms is realized.In the threshold model,when the threshold is higher than the critical value of information propagation,in order to propagate the information,in addition to increasing the initial propagation node,this paper solves this problem by combining the SI model with the threshold model,which improves the flexibility of the threshold model.In the information age,the information update speed is getting faster and faster,and the information is not always concerned.Finally,a new model is built by adding the information demise process to the threshold model to better describe the information dissemination process in the real network.