On a discrete generalized kinetic approach for modelling persuader’s influence in opinion formation processes

Modelling opinion formation by means of kinetic equations

“…which is very similar to (8). The functions P and D, the random variable η and the constant γ have the same meaning as in [77].…”

“…It is quite clear that the first Helbing model is a discrete velocity model. Note that this kind of model have been used later on to study opinion dynamics phenomena (for example, [6][7][8][9]). However, in the absence of spatial phenomena, their structure more remembers a dynamical system than a kinetic model.…”

Cluster formation in opinion dynamics: a qualitative analysis

“…In this section, we first discuss the main ingredients of the discrete active particle kinetic framework introduced in [5] (and then extended in [6]), which is suitable for the modelling of a population of pairwise interacting individuals characterized by their opinion. Then, we exploit this framework to construct a discrete version of the continuous bounded confidence model [8].…”

“…A main topic pertaining to this line of research is the formation of opinions within a group of interacting individuals. To explore when the resulting process leads to consensus and when it leads to polarization or fragmentation, methods taken from statistical mechanics [2,3,10,16], and from kinetic theory [5,6,17], have been employed, developed and adapted, often in conjunction with network structure concepts [11], and agent based approaches [19]. Particular interest has been dedicated to the so-called bounded confidence model, which was originally introduced in [8,18] (see also [12]) and then discussed and extended in various ways in a series of papers (see e.g.…”

“…In this paper, in particular, we make some progress towards the classification mentioned by Lorenz. In other words, employing a general framework, which we introduced in [5] for the construction of opinion dynamics models, we formulate a discrete version of the bounded confidence model, the term "discrete" referring to the possible values of the opinion variable (see also [2]). This version is expressed by a twoparameter family of systems of ordinary differential equations, where the two parameters are the number…”