{
  "abstract": "We study a nonlinear opinion dynamics model for stubborn individuals in time-varying signed cooperation–competition networks. The model incorporates nonlinear response functions, stochastic perturbations, and memory effects within a unified dynamical framework. We establish a uniform boundedness result under bounded external perturbations and derive a sufficient condition for contraction of trajectory differences based on the Lipschitz property of the nonlinear response and the interaction strengths. Polarization is characterized through a variance-based indicator together with the observed cluster structure. Numerical simulations illustrate the effects of nonlinear response strength, temporal network variability, stochastic perturbations, and memory mechanisms on convergence, clustering, and polarization-like behavior. An additional robustness test on the empirical Epinions signed social network shows that the qualitative dependence on nonlinear response strength persists under a large-scale heterogeneous topology. The proposed framework provides a mathematical and mechanism-based approach for analyzing nonlinear collective dynamics in heterogeneous signed networks.",
  "abstract_shown": true,
  "affiliations": [
    "School of Information Engineering, Information Engineering College, Hangzhou Dianzi University, Hangzhou 310005, China",
    "School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Qian Zhou"
    },
    {
      "affs": [
        1
      ],
      "name": "Yu Wang",
      "orcid": "0009-0003-0782-9989"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/27jjes5tanhyg.bib",
  "cited_by": 0,
  "doi": "10.3390/math14193611",
  "fulltext_url": null,
  "id": "27jjes5tanhyg",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/19/3611",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "3109|Opinion Dynamics and Social Influence"
    ]
  ],
  "openalex": "W7220428220",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/27jjes5tanhyg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14193611",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/19/3611"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3109|Opinion Dynamics and Social Influence",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Nonlinear Opinion Dynamics of Stubborn Individuals in Time-Varying Cooperation–Competition Networks",
  "title_text": "Nonlinear Opinion Dynamics of Stubborn Individuals in Time-Varying Cooperation–Competition Networks",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/27jjes5tanhyg",
  "venue": "Mathematics",
  "versions": []
}