Mathematical modeling analysis proves asymptotic convergence to consensus in two populations interacting via leaders with time delays, suggesting robust alignment across lagging networks.
We study a Hegselmann–Krause type opinion formation model for a system of two populations. The two groups interact with each other via subsets of individuals, namely, the leaders, and natural time delay effects are considered. By using careful estimates of the system's trajectories, we are able to prove an asymptotic convergence to consensus result. Some numerical tests illustrate the theoretical result and point out some possible applications.
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Cicolani et al. (2024) studied this question.
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