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

TL;DR

This paper introduces a continuous opinion dynamics model that incorporates population growth, analyzing how growth rates and incoming opinions influence long-term behavior, with well-posedness and asymptotic results for both the PDE and kinetic formulations.

Contribution

It presents a novel continuous opinion model accounting for population growth and boundary conditions, with well-posedness and asymptotic analysis for both PDE and kinetic versions.

Findings

Model well-posedness established

Long-term behavior influenced by growth rate and boundary conditions

Kinetic model analysis confirms PDE results

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.