Nonlinear Opinion Dynamics of Stubborn Individuals in Time-Varying Cooperation–Competition Networks
- 1School of Information Engineering, Information Engineering College, Hangzhou Dianzi University, Hangzhou 310005, China
- 2School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
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.
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BibTeX
@article{zhou2026nonlinear,
title = {{Nonlinear Opinion Dynamics of Stubborn Individuals in Time-Varying Cooperation–Competition Networks}},
author = {Qian Zhou and Yu Wang},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14193611},
url = {https://www.mdpi.com/2227-7390/14/19/3611},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Nonlinear Opinion Dynamics of Stubborn Individuals in Time-Varying Cooperation–Competition Networks
AU - Qian Zhou
AU - Yu Wang
PY - 2026
DA - 2026/10/05
JO - Mathematics
DO - 10.3390/math14193611
UR - https://www.mdpi.com/2227-7390/14/19/3611
AB - 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.
SN - 2227-7390
ER -