Opinion dynamics with Lotka-Volterra type interactions
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.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2018
- DOI:
- 10.48550/arXiv.1811.05937
- arXiv:
- arXiv:1811.05937
- Bibcode:
- 2018arXiv181105937A
- Keywords:
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- Mathematics - Probability;
- 60K35;
- 60K37;
- 62P25
- E-Print:
- 30 pages, 2 figures