On the Optimal Control of Opinion Dynamics on Evolving Networks

Abstract

In this work we are interested in the modelling and control of opinion dynamics spreading on a time evolving network with scale-free asymptotic degree distribution. The mathematical model is formulated as a coupling of an opinion alignment system with a probabilistic description of the network. The optimal control problem aims at forcing consensus over the network, to this goal a control strategy based on the degree of connection of each agent has been designed. A numerical method based on a model predictive strategy is then developed and different numerical tests are reported. The results show that in this way it is possible to drive the overall opinion toward a desired state even if we control only a suitable fraction of the nodes.

Opinion modeling on social media and marketing aspects

“…In these works it is shown, mainly through simulations, how agents with a certain stubbornness can affect the process of consensus formation, especially as far as the kind of expected equilibria that could arise due to their influence and the time needed to convergence are concerned. Last, to stress the importance of understanding opinion dynamics in the modern societies, we quote the recent attempts to investigate the process of opinion formation in presence of uncertain interactions between agents [37] and to act on it by means of suitable control strategies [2,3].…”

Recent Advances in Opinion Modeling: Control and Social Influence

“…In several recent works additional variables have been introduced quantifying relevant indicators for the spreading of opinions [9,10,31,54,58,91]. In this class of models the opinion dynamics depends on an additional parameter, continuous or discrete, which influences the binary exchanges.…”

“…, cmax} is the discrete variable describing the number of connections and t ∈ R + denotes as usual the time variable. For each time t ≥ 0 the marginal density 9) defines the evolution of the number of connections of the agents or equivalently the degree distribution of the network. In the sequel we assume that the total number of agents is conserved, i.e.…”

Reducing Complexity of Multiagent Systems with Symmetry Breaking: An Application to Opinion Dynamics with Polls

“…In order to bypass these difficulties of the theory, we propose a multiscale approach based on the hybridization of a reduced particle model, i.e. a model of type (4) with N * N agents, with the Fokker-Planck equation (15). The latter is meant to replace the remaining larger part of the agents that are not represented individually.…”

“…Multiscale model. Now we explore the possibility of reducing the number of agents of the particle model, i.e., to take N * N , while still keeping a good agreement with the reference full particle model (4) thanks to the multiscale model discussed in Section 4. In essence, with the aid of the continuous model we want to recover reliable statistics of the final vote V by tracking a much lower number of individuals than the total size N of the population and using only them to perform both the intermediate polls and the final evaluation of V .…”