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arXiv · 2505.19791

Opinion dynamics for an increasing population of agents. A symmetric continuous agent model

Ioannis Markou
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Abstract

In this paper we formulate a continuous opinion model that takes into account population growth, i.e. increase with time in the number of interacting agents $N(t)$. In our setting the population growth is governed by a generic growth rate function $b(t, N(t))$. The two main components of our model are the growth rate $b(t, N(t))$, as well as the opinions of the incoming agents which are modeled in our system as boundary conditions in a free boundary problem. We give results on the well-posedness of the model and results that showcase how these two components affect the long time asymptotic behavior of our system. Moreover, we provide a kinetic (probabilistic) description of our model and give results on well-posedness and asymptotics for the kinetic model.

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Ioannis Markou. 2025-05-26. Opinion dynamics for an increasing population of agents. A symmetric continuous agent model. https://arxiv.org/abs/2505.19791

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