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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

Partial differential equations with Robin boundary condition in online social networks

Pages: 1609 - 1624, Volume 20, Issue 6, August 2015      doi:10.3934/dcdsb.2015.20.1609

 
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Guowei Dai - Department of Mathematics, Northwest Normal University, Lanzhou, 730070, China (email)
Ruyun Ma - Department of Mathematics, Northwest Normal University, Lanzhou, 730070, China (email)
Haiyan Wang - School of Mathematical and Natural Sciences, Arizona State University, Phoenix, AZ 85069, United States (email)
Feng Wang - School of Mathematical and Natural Sciences, Arizona State University, Phoenix, AZ 85069, United States (email)
Kuai Xu - School of Mathematical and Natural Sciences, Arizona State University, Phoenix, AZ 85069, United States (email)

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.

Keywords:  Bifurcation, stability, diffusive logistic model, online social networks, indefinite weight, Robin boundary condition.
Mathematics Subject Classification:  Primary: 34C23, 35K57; Secondary: 90B10.

Received: February 2014;      Revised: January 2015;      Available Online: June 2015.

 References