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2019 Opinion dynamics with Lotka-Volterra type interactions
Michele Aleandri, Ida G. Minelli
Electron. J. Probab. 24: 1-31 (2019). DOI: 10.1214/19-EJP373

Abstract

We investigate a class of models for opinion dynamics in a population with two interacting families of individuals. Each family has an intrinsic mean field “Voter-like” dynamics which is influenced by interaction with the other family. The interaction terms describe a cooperative/conformist or competitive/nonconformist attitude of one family with respect to the other. We prove chaos propagation, i.e., we show that on any time interval $[0,T]$, as the size of the system goes to infinity, each individual behaves independently of the others with transition rates driven by a macroscopic equation. We focus in particular on models with Lotka-Volterra type interactions, i.e., models with cooperative vs. competitive families. For these models, although the microscopic system is driven a.s. to consensus within each family, a periodic behaviour arises in the macroscopic scale.

In order to describe fluctuations between the limiting periodic orbits, we identify a slow variable in the microscopic system and, through an averaging principle, we find a diffusion which describes the macroscopic dynamics of such variable on a larger time scale.

Citation

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Michele Aleandri. Ida G. Minelli. "Opinion dynamics with Lotka-Volterra type interactions." Electron. J. Probab. 24 1 - 31, 2019. https://doi.org/10.1214/19-EJP373

Information

Received: 15 November 2018; Accepted: 16 October 2019; Published: 2019
First available in Project Euclid: 6 November 2019

zbMATH: 07142916
MathSciNet: MR4029425
Digital Object Identifier: 10.1214/19-EJP373

Subjects:
Primary: 60K35, 60K37, 62P25

JOURNAL ARTICLE
31 PAGES


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Vol.24 • 2019
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