From individual interactions to collective patterns: A mathematical approach
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A mathematical approach is here discussed, addressed to try and explain the emergence of collective properties of socio-economic systems with a large number of individuals, based on the knowledge of pairwise individual interactions. In particular, two dierent issues, namely the opinion formation and the taxation and redistribution process, are considered. For each of them an abstract framework, in fact a system of nonlinear ordinary dierential equations, is proposed, which describes the evolution in time of a suitably discretized distribution function. The framework is then exploited to design and investigate speci c models. The outputs of computational simulations which illustrate the asymptotic properties of these models are reported.