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Spreading-vanishing dichotomy in information diffusion in online social networks with intervention

  • * Corresponding author: Jingli Ren

    * Corresponding author: Jingli Ren 
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  • In this paper, multiple information diffusion in online social networks with free boundary condition is investigated. We prove a spreading-vanishing dichotomy for the problem: i.e., either at least one piece of information lasts forever or all information suspend in finite time. The criterion for spreading and vanishing is established, it is related to the initial spreading area and the expansion capacity. We also obtain several cases of the asymptotic behavior of the information under different conditions. When the information spreads, we provide some upper and lower bounds of the spreading speed corresponding to different cases of asymptotic behavior of the information. In addition, numerical examples are given to illustrate the impacts of the initial spreading area and the expansion capacity on the free boundary, and all cases of the asymptotic behavior of the information.

    Mathematics Subject Classification: Primary: 35K20, 35R35; Secondary: 35B40.


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  • Figure 1.  The relationship among three information

    Figure 2.  $u, v$ and $w$ all vanish

    Figure 3.  $u, v$ and $w$ all spread

    Figure 4.  $u, v$ and $w$ all spread

    Figure 5.  $u, v$ and $w$ all spread

    Figure 6.  $u$ and $v$ vanish, $w$ spreads

    Figure 7.  $u$ vanishes, $v$ and $w$ spread

    Figure 8.  $v$ vanishes, $u$ and $w$ spread

    Figure 9.  $u, v$ and $w$ all spread

    Figure 10.  The density of influenced users of information A varies with the increase of the intervention rate $c_{1}$ for (A) and with the increase of the competition rate $b_{1}$ for (B)

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