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<p>Considering the complex psychological state reflected by user groups when facing rumors, this paper proposes a delayed rumor propagation model within heterogeneous networks that explicitly incorporates user conformity tendencies and psychological resilience mechanisms.&#xa0;Firstly, we prove the positivity and boundedness of the model solution, and calculate the basic reproduction number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {R_{0}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">R</mi> <mn mathvariant="script">0</mn> </msub> </math></EquationSource> </InlineEquation>. At the same time, the local linearization method and comparison principle are employed to analyze the stability of the rumor free equilibrium point (RFEP). Secondly, the dynamic evolution of the model is explored under both single and dual psychological states. By using the Lyapunov function method, the global asymptotic stability (G-stability) of the rumor equilibrium point (REP) is proved. In addition, several complex network-based immune control strategies and optimal control method are proposed to curb the spread of rumors. Finally, through comprehensive numerical simulations and a real-world case study, we validate the theoretical findings and conduct a comparative analysis of diverse control strategies.</p>

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The dynamics and control of rumor propagation model with conformity psychology and psychological defense in heterogeneous networks

  • 期刊论文

  • 发表日期：

    2026年1月7日

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  • Shuzhen Yu,
  • Li Yang,
  • Lishan Liu,
  • Zhiyong Yu,
  • Haijun Jiang

摘要

Considering the complex psychological state reflected by user groups when facing rumors, this paper proposes a delayed rumor propagation model within heterogeneous networks that explicitly incorporates user conformity tendencies and psychological resilience mechanisms. Firstly, we prove the positivity and boundedness of the model solution, and calculate the basic reproduction number \(\mathcal {R_{0}}\) R 0 . At the same time, the local linearization method and comparison principle are employed to analyze the stability of the rumor free equilibrium point (RFEP). Secondly, the dynamic evolution of the model is explored under both single and dual psychological states. By using the Lyapunov function method, the global asymptotic stability (G-stability) of the rumor equilibrium point (REP) is proved. In addition, several complex network-based immune control strategies and optimal control method are proposed to curb the spread of rumors. Finally, through comprehensive numerical simulations and a real-world case study, we validate the theoretical findings and conduct a comparative analysis of diverse control strategies.