Breaking Consensus in Kinetic Opinion Formation Models on Graphons
arXiv:2403.14431 · doi:10.1007/s00332-024-10060-4
Abstract
In this work we propose and investigate a strategy to prevent consensus in kinetic models for opinion formation. We consider a large interacting agent system, and assume that agent interactions are driven by compromise as well as self-thinking dynamics and also modulated by an underlying static social network. This network structure is included using so-called graphons, which modulate the interaction frequency in the corresponding kinetic formulation. We then derive the corresponding limiting Fokker Planck equation, and analyze its large time behavior. This microscopic setting serves as a starting point for the proposed control strategy, which steers agents away from mean opinion and is characterised by a suitable penalization depending on the properties of the graphon. We show that this minimalist approach is very effective by analyzing the quasi-stationary solutions mean-field model in a plurality of graphon structures. Several numerical experiments are also provided to show the effectiveness of the approach in preventing the formation of consensus steering the system towards a declustered state.
Changed to align to the in-print version
References in corpus (17)
- Emergence of scaling in random networks
- The structure and function of complex networks
- Sociophysics: A review of Galam models
- The role of network topology on extremism propagation with the Relative Agreement opinion dynamics
- On a kinetic model for a simple market economy
- Boltzmann type control of opinion consensus through leaders
- Graphon Control of Large-scale Networks of Linear Systems
- Opinion modeling on social media and marketing aspects
- Opinion dynamics: inhomogeneous Boltzmann-type equations modelling opinion leadership and political segregation
- Noisy bounded confidence models for opinion dynamics: the effect of boundary conditions on phase transitions
- Kinetic models of collective decision-making in the presence of equality bias
- Hydrodynamic models of preference formation in multi-agent societies
- Particle interactions mediated by dynamical networks: assessment of macroscopic descriptions
- A data-driven kinetic model for opinion dynamics with social network contacts
- On sparsity, power-law and clustering properties of graphex processes
- A note on Fokker-Planck equations and graphons
- Network-based kinetic models: Emergence of a statistical description of the graph topology