Well-posedness of the limiting equation of a noisy consensus model in opinion dynamics

DOI10.1016/j.jde.2017.02.036zbMath1367.35181arXiv1510.06487OpenAlexW2963075057MaRDI QIDQ525973

Chu Wang, Bernard Chazelle, Qianxiao Li, Quan-sen Jiu

Publication date: 8 May 2017

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.06487

zbMATH Keywords

global stabilitywell-posednessnonlinear Fokker-Planck equationHegselmann-Krause model

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Stability in context of PDEs (35B35) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Models of societies, social and urban evolution (91D10) Weak solutions to PDEs (35D30) Integro-partial differential equations (35R09) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Fokker-Planck equations (35Q84)

Related Items (10)

Noisy Hegselmann-Krause systems: phase transition and the \(2R\)-conjecture ⋮ Toward a Theory of Markov Influence Systems and their Renormalization ⋮ Well-posedness and stationary solutions of McKean-Vlasov (S)PDEs ⋮ Online parameter estimation for the McKean-Vlasov stochastic differential equation ⋮ Parameter estimation of discretely observed interacting particle systems ⋮ Shifting Consensus in a Biased Compromise Model ⋮ Consensus for Hegselmann–Krause type models with time variable time delays ⋮ Long-time behaviour and phase transitions for the McKean-Vlasov equation on the torus ⋮ Nonparametric estimation for interacting particle systems: McKean-Vlasov models ⋮ The LAN property for McKean-Vlasov models in a mean-field regime

Cites Work

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• Opinion dynamics under the influence of radical groups, charismatic leaders, and other constant signals: a simple unifying model
• Initiation of slime mold aggregation viewed as an instability
• Kinetic models of opinion formation
• A non-Maxwellian steady distribution for one-dimensional granular media
• Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
• An algorithmic approach to collective behavior
• Global existence for a nonlocal and nonlinear Fokker-Planck equation
• Consensus convergence with stochastic effects
• Noisy Hegselmann-Krause systems: phase transition and the \(2R\)-conjecture
• ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS
• LARGE TIME ASYMPTOTICS OF NONLINEAR DRIFT-DIFFUSION SYSTEMS WITH POISSON COUPLING
• An Eulerian Approach to the Analysis of Krause's Consensus Models
• Heterophilious Dynamics Enhances Consensus
• On the convergence of the Hegselmann-Krause system
• ON THE CONSENSUS THRESHOLD FOR THE OPINION DYNAMICS OF KRAUSE–HEGSELMANN
• Continuous-Time Average-Preserving Opinion Dynamics with Opinion-Dependent Communications
• Diffusive Influence Systems
• Blow-up in multidimensional aggregation equations with mildly singular interaction kernels
• Kramers and Non-Kramers Phase Transitions in Many-Particle Systems with Dynamical Constraint
• Boltzmann and Fokker–Planck equations modelling opinion formation in the presence of strong leaders
• On the spatially homogeneous landau equation for hard potentials part ii : h-theorem and applications
• On Krause's Multi-Agent Consensus Model With State-Dependent Connectivity
• On the control through leadership of the Hegselmann–Krause opinion formation model
• Coordination of groups of mobile autonomous agents using nearest neighbor rules
• Stability of multiagent systems with time-dependent communication links
• On Synchronous Robotic Networks—Part II: Time Complexity of Rendezvous and Deployment Algorithms
• Opinion dynamics: inhomogeneous Boltzmann-type equations modelling opinion leadership and political segregation
• The noisy Hegselmann-Krause model for opinion dynamics

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