Control of kinetic opinion dynamics in popularity-adaptive social networks

TL;DR

A novel feedback mechanism in which opinion affects the formation of contacts is introduced, incorporating a class of control laws in order to promote interactions with popular individuals and amplify dominant opinions in popularity-adaptive social networks.

Abstract

This paper presents a mathematical model for opinion dynamics in popularity-adaptive social networks, where both opinion spreading and the evolution of social media contacts depend on agents' popularity and the prominence of their views. While previous approaches accounted for the influence of popularity on opinion dynamics, we introduce a novel feedback mechanism in which opinion affects the formation of contacts. Within a kinetic modeling framework, we describe the evolution of the coupled dynamics of opinions and network structure, incorporating a class of control laws in order to promote interactions with popular individuals and amplify dominant opinions. Such control strategies are introduced to influence both opinion formation and connectivity, representing interventions such as awareness campaigns or moderation policies. Numerical results show how control strategies can mitigate polarization, foster consensus, or guide opinion distributions in dynamically evolving networks.

Figures (13)

• Figure 1: Plot of $\Psi(s)$. The red lines represent the bounds of the function when $\mu = 0.1$.
• Figure 2: Test 1. Joint density $f(c,v,0)$ at the initial time.
• Figure 3: Test 1. Time evolution of the joint density $f(c,v,t)$ in the $(v,c)$ plane for different control strategies. Each panel shows snapshots at times $t=1, 5, {\color{black}{15}}, 50$. (a) uncontrolled dynamics; (b) control on contacts; (c) control on opinions; (d) both controls active.
• Figure 4: Test 1. Time evolution of the marginal distributions of contacts and opinions at different times for different control strategies. Each panel shows both distributions together: contacts (left) and opinions (right). (a) uncontrolled dynamics; (b) control on contacts; (c) control on opinions; (d) both controls active.
• Figure 5: Test 1. Time evolution of the mean number of contacts $m_c(t)$ (left panel) and the mean opinion $m_v(t)$ (right panel) over the interval $[0,T]$. In both panels we report the temporal averages corresponding to the four scenarios (a)--(d), each represented with a different colour.

Theorems & Definitions (4)

• Remark 2.1: Time discrete functional and continuous limit.
• Remark 2.2: Conditional equilibria and quasi-stationary behaviour
• Remark 3.1: Structure of the optimal control term
• Remark 3.2: Macroscopic moment dynamics