Methodology

Complex Systems and Society: Modeling and Simulation by Nicola Bellomo, Giulia Ajmone Marsan, Andrea Tosin

By Nicola Bellomo, Giulia Ajmone Marsan, Andrea Tosin

This paintings goals to foster the interdisciplinary discussion among mathematicians and socio-economic scientists. interplay between students and practitioners usually coming from assorted learn parts is critical greater than ever so as to larger comprehend many real-world difficulties we are facing this present day. at the one hand, mathematicians desire economists and social scientists to higher tackle the methodologies they layout in a extra reasonable means; nonetheless, economists and social scientists have to be conscious of sound mathematical modelling instruments for you to comprehend and, finally, resolve the advanced difficulties they stumble upon of their study. With this target in brain, this paintings is designed take into consideration a multidisciplinary technique that may motivate the move of data, rules, and technique from one self-discipline to the opposite. particularly, the paintings has 3 major subject matters: Demystifying and unravelling advanced structures; Introducing types of person behaviours within the social and monetary sciences; Modelling socio-economic sciences as advanced dwelling platforms. particular instruments tested within the paintings contain a lately built modelling strategy utilizing stochastic video game idea in the framework of statistical mechanics and progressing as much as modeling Darwinian evolution. certain realization is additionally dedicated to social community thought as a basic device for the knowledge of socio-economic systems.​

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Moreover, we observe that the cooperative and competitive rules 36 3 Modeling Cooperation and Competition in Socio-Economic Systems Fig. 2 Game dynamics which do not preserve, in general, the average wealth of the society. (a) Wealth-productive dynamics. (b) Wealth-dissipative dynamics a wealth status u b wealth status u particle 1 particle 2 described above are consistent with the preservation of the average wealth of the society, if the impoverishment of a particle and the simultaneous enrichment of its interacting companion are of the same extent.

M, have different meanings in each subsystem. Mutations and selections. These events are respectively related to transitions across functional subsystems, accounted for by the table of games, and to proliferative interactions, modeled by the operators P p . Their modeling requires, 32 2 Mathematical Tools for Modeling Social Complex Systems in general, that the influence of the outer environment on the conservative interactions be carefully analyzed. • Multiscale essence. The modeling of aforementioned terms η , C , and P is generally obtained by a mainly phenomenological approach at the microscopic scale.

Therefore disappearance, splitting, or creation of functional subsystems can be additional sources of nonlinearity in the equations. The previous arguments drop a hint that interactions at the microscale can be strongly characterized by various types of nonlinearities. Consequently, in most cases the evolution equations feature further nonlinearities besides the standard quadratic one due to the product of the distribution functions in the terms C p and P p . The mathematical structures proposed in the preceding sections are still valid but the following notations are worth being introduced for stressing such constitutive nonlinearities: ∗ η p∗ p [f](u∗ , u∗ ), ∗ C p∗ p [f](u∗ → u; p|u∗ , u∗ ), ∗ and P p∗ p [f](u∗ , u∗ ; u, p).

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