Methods and Applications of Analysis

Volume 29 (2022)

Number 3

The inverse problem for the reconstruction of the weight functions in a socio-economic system modelled by the discrete thermostatted kinetic framework

Pages: 249 – 264

DOI: https://dx.doi.org/10.4310/MAA.2022.v29.n3.a2

Authors

Bruno Carbonaro (Dipartimento di Matematica e Fisica, Università degli Studi della Campania, Caserta, Italy)

Marco Menale (Dipartimento di Matematica e Fisica, Università degli Studi della Campania, Caserta, Italy)

Abstract

The aim of the paper is threefold. First of all, since our main goal is to apply the discrete thermostatted kinetic framework to a socio-economic system whose space of microscopic states is discrete, we discuss the inverse problem (see the Introduction) in the discrete case. Next, we propose an example of a socio-economic system of the above kind, paying special attention to the choice of a particularly meaningful and plausible initial probability distribution on the state space. Finally, we sketch a first simple numerical simulation of the evolution of the system, just in order to show that the appropriate choice of initial conditions leads to a forecast of such evolution which seems to fit the experienced evolutions of western societies at present.

Keywords

nonlinear ordinary differential equations, thermostatted framework, modeling, inverse problem

2010 Mathematics Subject Classification

34A55, 37A50, 37N40, 91B74

The full text of this article is unavailable through your IP address: 172.17.0.1

The research of M.M. has been carried out under the auspices of GNFM (National Group of Mathematical-Physics) of INDAM (National Institute of Advanced Mathematics).

Received 8 May 2020

Accepted 25 February 2022

Published 21 March 2023