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Dynamical behaviors and event-triggered impulsive control of a delayed information propagation model based on public sentiment and forced silence

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Abstract

Adverse information can spread through emotional expression to cause public panic and social instability. The network regulators may limit the spread by force silently. This paper aims to capture the effects of public sentiment and forced silence on information propagation. To this end, the paper proposes a class of SFPFNR information propagation models with time delays and a forced silence function on a heterogeneous network. In addition, event-triggered impulsive control mechanism is designed. Combined with forced silence, the paper creates a dual control mechanism. Next, the mean-field principle is used to calculate the basic reproduction number \(R_{0}\) and then prove the existence of the equilibrium point \(E^{*}\). By constructing the Lyapunov function and applying the comparison principle, the global and local stability of the system are then discussed. Besides, we perform extensive numerical simulations to verify the theoretical conclusions. The results show that time delays do not affect system stability, and negative emotions are crucial for large-scale information transmission. Finally, the model is applied to the actual case and shows a significant improvement in prediction accuracy compared with the SIR model. The RMSE decreases from 0.3234 to 0.0664. Therefore, the model can guide social media management and information dissemination regulation.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: The data that support the findings of this study are available in the Sects. 4 and 5.]

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Acknowledgements

This study was supported by the National Natural Science Foundation of China (No. 71701036).

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Authors and Affiliations

  1. School of Economics, Northeastern University at Qinhuangdao, Qinhuangdao, 066004, Hebei, China

    Yuanyuan Ma

  2. School of Management, Northeastern University at Qinhuangdao, Qinhuangdao, 066004, Hebei, China

    Leilei Xie, Shu Liu & Xinyu Chu

  3. School of Business Administration, Northeastern University, Shenyang, 110819, Liaoning, China

    Yuanyuan Ma, Leilei Xie, Shu Liu & Xinyu Chu

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  1. Yuanyuan Ma
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Correspondence to Yuanyuan Ma.

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Ma, Y., Xie, L., Liu, S. et al. Dynamical behaviors and event-triggered impulsive control of a delayed information propagation model based on public sentiment and forced silence. Eur. Phys. J. Plus 138, 979 (2023). https://doi.org/10.1140/epjp/s13360-023-04589-8

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