基于传染力和连接强度函数的股市传闻扩散广义模型

A Generalized Rumour Spreading Model Based on Functions of Infectivity and Connective Strength in Stock Market

引入节点的非线性传染力函数和相邻节点间连边的连接强度函数,构建基于股市投资者复杂网络的传闻扩散广义模型。通过对模型稳态的动力学行为的理论解析以及进一步的数值仿真发现:传染力指数?和连接强度函数指数?对投资者网络上的传闻扩散行为有明显的影响;通过调节指数?和?的值,可使标准模型中消失的传闻阈值在广义模型中重现;与连接强度指数?相比,传染力指数?对传闻阈值的影响效应更显著。

The stock market is a significant part of the modern financial system,and its stabilityis essential tosustainableeconomic development in a country. All kinds of rumors are prevalent in the stock market and influencethe stability of the stock market. In fact, market rumors can result in the fluctuation in stock markets.The realization of whichpredominantly depends on rumor diffusion between investors.Thus, it is important to study the diffusion phenomenon between investors of the rumors. In this paper, we introduce a generalized model for the spread of rumorsand analytically and numericallyinvestigate the dynamic behaviorsof the model in the complex networks of investors in the stock market. The previous rumorsspreading models are almost based on the following assumptions： the transmission rate of a rumoris a constant, and each spreadercanestablish contacts with all his（her） neighbors within onetime step, that is to say, each node＇s infectivity equals its degree. However,these assumptions may be inappropriate in the real life, where the transmission rate is different among individuals depending on their intimacy, confidence, kinship, etc. Anindividual cannot make contact with all of his closefriends（connected neighbors） simultaneously. In order to solve these problems, we introduce a connectivity strength function（CSF） between connected nodes, which represent the intimacy, confidence, kinship, etc., between individuals, and a nonlinear function for the infectivity of nodes to take control of thenumber of contacts that a spreading node generates within onetime step. Then, based on the standard rumorspreading model, we propose a generalized rumor spreading model, with the characteristics of nonlinear infectivity and connectivity strength for investor networks of stock market in the first part. In the second part, by using the mean-fieldequations that describe thedynamics of the generalized model for the spread of rumorson complex networks of investors in stock market, we analyticallyinvestigatethe stationary state and the critical behaviorof our model. Especially, for both infectivityfunction and connectivity strength function taking power-law form, a furtheranalysis for the rumorthreshold of the generalized rumorspreading model on finite investor networks is carried out. In the third part, the analytical results we obtain areverified withthe necessary numerical simulations. We show that as the result of different values of both the infectivity＇s exponent and the CSF＇s exponent, the time-dependent behaviorsof both the standard rumormodel and the generalized model present significant difference. We also find that one can adjust the infectivity＇s exponent and theC SF＇s exponentto rebuild the rumorthreshold which is absent for the standard rumorspreading model. The critical boundary of the rumorthreshold depends on the infectivity＇s exponent and the CSF＇s exponent for a given topology of investor networks. Furthermore, comparing the CSF＇s exponent, the infectivity＇s exponent has a dominant impact on the rumorthreshold, which meanscontrolling the contacts of individuals is more important than the degree-biased transmission rate. These findings provide a new theoretical perspective for the listed company and the supervision department to conduct effective supervision and control of the rumorspreadinginthe stock market.