Macroscopic Noisy Bounded Confidence Models with Distributed Radical Opinions

In this article, we study the nonlinear Fokker-Planck (FP) equation that arises as a mean-field (macroscopic) approximation of bounded confidence opinion dynamics, where opinions are influenced by environmental noises and opinions of radicals (stubborn individuals). The distribution of radical opinions serves as an infinite-dimensional exogenous input to the FP equation, visibly influencing the steady opinion profile. We establish mathematical properties of the FP equation. In particular, we (i) show the well-posedness of the dynamic equation, (ii) provide existence result accompanied by a quantitative global estimate for the corresponding stationary solution, and (iii) establish an explicit lower bound on the noise level that guarantees exponential convergence of the dynamics to stationary state. Combining the results in (ii) and (iii) readily yields the input-output stability of the system for sufficiently large noises. Next, using Fourier analysis, the structure of opinion clusters under the uniform initial distribution is examined. Specifically, two numerical schemes for identification of order-disorder transition and characterization of initial clustering behavior are provided. The results of analysis are validated through several numerical simulations of the continuum-agent model (partial differential equation) and the corresponding discrete-agent model (interacting stochastic differential equations) for a particular distribution of radicals

Opinion dynamics on directed complex networks

We propose and analyze a mathematical model for the evolution of opinions on directed complex networks. Our model generalizes the popular DeGroot and Friedkin-Johnsen models by allowing vertices to have attributes that may influence the opinion dynamics. We start by establishing sufficient conditions for the existence of a stationary opinion distribution on any fixed graph, and then provide an increasingly detailed characterization of its behavior by considering a sequence of directed random graphs having a local weak limit. Our most explicit results are obtained for graph sequences whose local weak limit is a marked Galton-Watson tree, in which case our model can be used to explain a variety of phenomena, e.g., conditions under which consensus can be achieved, mechanisms in which opinions can become polarized, and the effect of disruptive stubborn agents on the formation of opinions

Bounded Confidence Evolution of Opinions and Actions in Social Networks

This work was supported in part by the National Natural Science Foundation of China under Grant 71991460, Grant 71991465, Grant 71871149, Grant 71910107002, and Grant 71725001; in part by the Research Foundation of Education Bureau of Hunan Province, China, under Grant 20B147; and in part by the Spanish State Research Agency under Project PID2019-103880RB-I00/AEI/10.13039/501100011033.Inspired by the continuous opinion and discrete action (CODA) model, bounded confidence and social networks, the bounded confidence evolution of opinions and actions in social networks is investigated and a social network opinions and actions evolutions (SNOAEs) model is proposed. In the SNOAE model, it is assumed that each agent has a CODA for a certain issue. Agents’ opinions are private and invisible, that is, an individual agent only knows its own opinion and cannot obtain other agents’ opinions unless there is a social network connection edge that allows their communication; agents’ actions are public and visible to all agents and impact other agents’ actions. Opinions and actions evolve in a directed social network. In the limitation of the bounded confidence, other agents’ actions or agents’ opinions noticed or obtained by network communication, respectively, are used by agents to update their opinions. Based on the SNOAE model, the evolution of the opinions and actions with bounded confidence is investigated in social networks both theoretically and experimentally with a detailed simulation analysis. Theoretical research results show that discrete actions can attract agents who trust the discrete action, and make agents to express extreme opinions. Simulation experiments results show that social network connection probability, bounded confidence, and the opinion threshold of action choice parameters have strong impacts on the evolution of opinions and actions. However, the number of agents in the social network has no obvious influence on the evolution of opinions and actions.National Natural Science Foundation of China (NSFC) 71991460 71991465 71871149 71910107002 71725001Research Foundation of Education Bureau of Hunan Province, China 20B147Spanish Government PID2019-103880RB-I00/AEI/10.13039/50110001103

Micro-macro dynamics of the online opinion evolution: an asynchronous network model approach

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.This paper investigates the complex relationship between endogenous and exogenous, deterministic and stochastic stimulating factors in public opinion dynamics. An asynchronous multi-agent network model is proposed to explore the interaction mechanism between individual opinions and the public opinion in online multi-agent network community, including both the micro and the macro patterns of opinion evolution. In addition, based on random network models, a novel algorithm is provided for opinion evolution prediction. The model property analysis and numerical experiments show that the proposed asynchronous multi-agent network model can assimilate and explain some interesting phenomena that are observed in the real world. Further case studies with numerical simulation and real-world applications confirm the feasibility and flexibility of the proposed model in public opinion analysis. The results challenge the common perception that mass media or opinion facilitators play the fundamental role in controlling the development trends of public opinion. This study shows that the formation and evolution of public opinion in the presence of opinion leaders depend also on an individual’s emotional inertia and conformity pressures from peers in the same topic group