Mean-field dynamics of the non-consensus opinion model

Abstract

In 2009, Shao et al. (Phys Rev Lett 103(1):018701, 2009) introduced the Non-consensus opinion (NCO) model, which allows different opinions to coexist in the steady state. We propose a mean-field-based dynamical model for the NCO model on networks with low degree correlation, which reveals the mechanism of opinion formation in the NCO model. This mean-field model provides a new way of estimating important system properties such as the fraction of a certain opinion F, the critical threshold fc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_c$$\\end{document}, and the size of the largest connected cluster for a given opinion s1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s_1$$\\end{document}. It offers an accurate estimation in less time than the Monte Carlo simulations. The scale invariance of the NCO model is discussed. The variation in the degree of nodes holding different opinions in the dynamics of the NCO model is investigated. The trends in the dynamics of the NCO model are also revealed. This approach can be applied to real-world social networks, providing a method of analyzing opinion dynamics in human society.