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EnglishIn 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.
| Titolo: | Consensus of the Hegselmann-Krause opinion formation model with time delay |
| Autori: | |
| Data di pubblicazione: | 2021 |
| Rivista: | |
| Handle: | http://hdl.handle.net/11697/153519 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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http://hdl.handle.net/11697/153519
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