Mathematical Analysis

  • Haiyan Wang
  • Feng Wang
  • Kuai Xu
Part of the Surveys and Tutorials in the Applied Mathematical Sciences book series (STAMS, volume 7)


In this chapter we discuss a free boundary problem for reaction-diffusion logistic equations in online social networks. Specifically, we discuss several bifurcation and stability results for a nonautonomous diffusive logistic model in online social networks with Robin boundary conditions. In addition, we present Hopf bifurcation and spatial patterns of an epidemic-like rumor model for online social networks. Finally, we present traveling wave solutions of diffusive models and give long-term propagation rates of information diffusion in online social networks.


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Haiyan Wang
    • 1
  • Feng Wang
    • 1
  • Kuai Xu
    • 1
  1. 1.School of Mathematical & Natural SciencesArizona State UniversityPhoenixUSA

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