A Simple Proof of Asymptotic Consensus in the Hegselmann--Krause and Cucker--Smale Models with Normalization and Delay

DOI10.1137/20M1341350zbMath1466.34073arXiv2005.13589OpenAlexW3123629326MaRDI QIDQ4983524

Jan Haskovec

Publication date: 20 April 2021

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.13589

zbMATH Keywords

long-time behaviorflockingCucker-Smale modelvariable delayHegselmann-Krause modelasymptotic consensus

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Asymptotic theory of functional-differential equations (34K25) Qualitative investigation and simulation of models involving functional-differential equations (34K60) Animal behavior (92D50)

Related Items (16)

Cucker-Smale model with time delay ⋮ Exponential Convergence Towards Consensus for Non-Symmetric Linear First-Order Systems in Finite and Infinite Dimensions ⋮ The delayed Cucker-Smale model with short range communication weights ⋮ Flocking in the Cucker-Smale model with self-delay and nonsymmetric interaction weights ⋮ Collective behavior for the delayed Cucker-Smale system in a harmonic potential field ⋮ The stochastic delayed Cucker-Smale system in a harmonic potential field ⋮ Cucker-Smale model with finite speed of information propagation: well-posedness, flocking and mean-field limit ⋮ Collision avoidance and asymptotic flocking in the delayed Cucker-Smale model with singular short range communication weights ⋮ Asymptotic behavior of the linear consensus model with delay and anticipation ⋮ Flocking analysis for a generalized Motsch-Tadmor model with piecewise interaction functions and processing delays. ⋮ Asymptotic flocking for the Cucker-Smale model with time variable time delays ⋮ Flocking of a thermodynamic Cucker-Smale model with local velocity interactions ⋮ Consensus for Hegselmann–Krause type models with time variable time delays ⋮ Generalized solutions to bounded-confidence models ⋮ Delay-dependent flocking dynamics of a two-group coupling system ⋮ Direct proof of unconditional asymptotic consensus in the Hegselmann–Krause model with transmission‐type delay

Cites Work

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• Heterophilious Dynamics Enhances Consensus
• A WELL-POSEDNESS THEORY IN MEASURES FOR SOME KINETIC MODELS OF COLLECTIVE MOTION
• A Cucker--Smale Model with Noise and Delay
• Consensus of the Hegselmann–Krause opinion formation model with time delay
• Consensus and Fragmentation of Opinions with a Focus on Bounded Confidence
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