Abstract
In recent years, online social networks such as Twitter, have become a major source of information exchange and research on information diffusion in social networks has been accelerated. Partial differential equations are proposed to characterize temporal and spatial patterns of information diffusion over online social networks. The new modeling approach presents a new analytic framework towards quantifying information diffusion through the interplay of structural and topical influences. In this paper we develop a non-autonomous diffusive logistic model with indefinite weight and the Robin boundary condition to describe information diffusion in online social networks. It is validated with a real dataset from an online social network, Digg.com. The simulation shows that the logistic model with the Robin boundary condition is able to more accurately predict the density of influenced users. We study the bifurcation, stability of the diffusive logistic model with heterogeneity in distance. The bifurcation and stability results of the model information describe either information spreading or vanishing in online social networks.
Highlights
Online social networking has indisputably become a forefront platform for information exchange in recent years
There is a wealth of research focusing on the measurement and analysis of network structures, user interactions, and traffic characteristics of social media with empirical approaches which utilize data mining and statistical modeling schemes
In this paper we develop a non-autonomous diffusive logistic model with indefinite weight and the Robin boundary condition to describe information diffusion in online social networks
Summary
Online social networking has indisputably become a forefront platform for information exchange in recent years. Bifurcation, stability, diffusive logistic model, online social networks, indefinite weight, Robin Boundary Condition. In this paper we develop a non-autonomous diffusive logistic model with indefinite weight and the Robin boundary condition to describe information diffusion in online social networks. Wang and Xu use partial differential equations built on intuitive cyber-distance among online users to study both temporal and spatial patterns of information diffusion process in social media. The PDE models for online social networks provide a new analytic framework towards a better understanding of information diffusion mechanisms by studying the interplay of structural and topical influences. Lei, Lin and the third author [18] proposed and studied the following free boundary model to describe the spreading of news in online social networks ut duxx r(t)u(1.
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