Stages

Numerous models have been proposed to describe the evolution of opinions in a population. These models are built from 2 parts: one describes the evolution of the opinions of two agents when they interact (with the underlying hypothesis that interactions tend to make opinions closer); the second describes the structure of interactions in the population, generally described by a network.

While many studies have focused on the impact of the network structure on how the opinions evolve, and on the possibility to reach a global consensus, few examine dynamical differences between models, for a fixed interaction structure. Studying such differences is however important to compare models to experiments, in order to discriminate between models and validate models.

The goal of the internship will thus be to define measures to describe the patterns of opinion evolution in a population, in a similar spirit as [3] in the case of spreading, and to investigate several models to show the discriminative power of these measures.

Numerous models have been proposed to describe the evolution of opinions in a population. These models are built from 2 parts: one describes the evolution of the opinions of two agents when they interact (with the underlying hypothesis that interactions tend to make opinions closer); the second describes the structure of interactions in the population, generally described by a network. While most studies consider such structures as fixed, they actually vary in time and need to be described through the framework of temporal networks.

Few studies have considered the impact of the temporality of interactions on the dynamics of opinions. The project will consist in the adaptation and simulation of models of opinion dynamics on temporal networks, given either by synthetic models or by empirical data sets (e.g. from SocioPatterns), as well as on randomized structures to examine the roles of the various temporal properties of the networks. The models will be further refined to take into account the diversity of social influence weights, and also to include adaptivity (feedback of the opinion differences on the network structure).

Chaotic dynamics, characterized by sensitivity to initial conditions, are ubiquitous in nature and arise across a wide range of scales and physical systems, from the Solar System to fluid dynamics, plasma physics, or the motion of artificial satellites orbiting the Earth. The existence of chaos has strong consequences for the predictability of future states of the dynamical system. Despite being deterministic, small uncertainties in the initial conditions can grow rapidly, limiting our ability to make reliable predictions in the long-term. This fundamental property has motivated the development of several computational methods for detecting and characterizing chaotic dynamics over the past several decades.