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arXiv · 1909.02795

Consensus of the Hegselmann-Krause opinion formation model with time delay

Young-Pil Choi·Alessandro Paolucci·Cristina Pignotti
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Abstract

In this paper, we study Hegselmann-Krause models with a time-variable time delay. Under appropriate assumptions, we show the exponential asymptotic consensus when the time delay satisfies a suitable smallness assumption. Our main strategies for this are based on Lyapunov functional approach and careful estimates on the trajectories. We then study the mean-field limit from the many-individual Hegselmann-Krause equation to the continuity-type partial differential equation as the number N of individuals goes to infinity. For the limiting equation, we prove global-in-time existence and uniqueness of measure-valued solutions. We also use the fact that constants appearing in the consensus estimates for the particle system are independent of N to extend the exponential consensus result to the continuum model. Finally, some numerical tests are illustrated.

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Young-Pil Choi, Alessandro Paolucci, Cristina Pignotti. 2019-09-06. Consensus of the Hegselmann-Krause opinion formation model with time delay. https://arxiv.org/abs/1909.02795

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