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App. Res. of Comp. Accepted Paper
Vol. 43, 2026 No. 2

Dynamics model of public opinion propagation in two-layer coupled networks under time-delay effect

Xu Huijie
Ma Jingke
School of Business, Henan University of Science and Technology, Luoyang Henan 471023, China
DOI: 10.19734/j.issn.1001-3695.2025.07.0248

Abstract

This study investigated the impact of time delays during information dissemination and extinction on public opinion evolution within an official-civilian dual-layer coupled network in social media environments. A dynamic framework coupling the Official Layer Network (OLN) and the Civilian Layer Network (CLN) was established. The research introduced time delay parameter τ to characterize the delay between official information release and public response. Stability theory and Hopf bifurcation analysis were employed to determine the existence and stability of system equilibria. The results reveal the existence of a critical time delay threshold τc. When τ < τc, the system remains asymptotically stable and public opinion gradually diminishes; when τ > τc, the system loses stability and undergoes Hopf bifurcation, and public opinion will exhibit periodic oscillations. Both the blocking rate and advancement rate of OLN can reduce the dissemination threshold R0, with the blocking rate playing a more significant role in controlling the spread of public opinion. Time delay critically influences the stability of the dual-layer network. Prompt official monitoring and intervention can effectively mitigate the risks of public opinion propagation.

Foundation Support

国家自然科学基金青年项目(72404079)
河南省软科学研究计划项目(222400410179)

Publish Information

DOI: 10.19734/j.issn.1001-3695.2025.07.0248
Publish at: Application Research of Computers Accepted Paper, Vol. 43, 2026 No. 2

Publish History

[2025-10-28] Accepted Paper

Cite This Article

徐会杰, 马静珂. 时滞效应下双层耦合网络舆情传播动力学模型 [J]. 计算机应用研究, 2026, 43 (2). (2025-11-04). https://doi.org/10.19734/j.issn.1001-3695.2025.07.0248. (Xu Huijie, Ma Jingke. Dynamics model of public opinion propagation in two-layer coupled networks under time-delay effect [J]. Application Research of Computers, 2026, 43 (2). (2025-11-04). https://doi.org/10.19734/j.issn.1001-3695.2025.07.0248. )

About the Journal

  • Application Research of Computers Monthly Journal
  • Journal ID ISSN 1001-3695
    CN  51-1196/TP

Application Research of Computers, founded in 1984, is an academic journal of computing technology sponsored by Sichuan Institute of Computer Sciences under the Science and Technology Department of Sichuan Province.

Aiming at the urgently needed cutting-edge technology in this discipline, Application Research of Computers reflects the mainstream technology, hot technology and the latest development trend of computer application research at home and abroad in a timely manner. The main contents of the journal include high-level academic papers in this discipline, the latest scientific research results and major application results. The contents of the columns involve new theories of computer discipline, basic computer theory, algorithm theory research, algorithm design and analysis, blockchain technology, system software and software engineering technology, pattern recognition and artificial intelligence, architecture, advanced computing, parallel processing, database technology, computer network and communication technology, information security technology, computer image graphics and its latest hot application technology.

Application Research of Computers has many high-level readers and authors, and its readers are mainly senior and middle-level researchers and engineers engaged in the field of computer science, as well as teachers and students majoring in computer science and related majors in colleges and universities. Over the years, the total citation frequency and Web download rate of Application Research of Computers have been ranked among the top of similar academic journals in this discipline, and the academic papers published are highly popular among the readers for their novelty, academics, foresight, orientation and practicality.

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