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Abstract
This editorial paper presents a special issue devoted to the development of mathematical tools from kinetic and swarms theory to the modeling and simulations of the dynamics of living systems constituted by very many interacting living entities. Applications refer to several fields: collective learning, behavioral economy, multicellular systems, vehicular traffic, and human crowds. A forward look to research perspectives is focused on the conceptual links between swarms methods and the kinetic theory approach.
Highlights
This paper presents the conceptual framework of the special issue “Kinetic Theory and Swarming
The special issue is devoted to report the research activity in the field by means of a selection of scientific articles, where mathematical tools of the kinetic theory and swarms dynamics can contribute to modeling and simulations of living systems
We mention with the aim of providing a fully detailed framework the kinetic theory approach developed by mean field and Fokker–Plank models [11], where a variety of interesting models mainly on social dynamics are reported and implemented by sharp numerical tools
Summary
This paper presents the conceptual framework of the special issue “Kinetic Theory and Swarming. The special issue is devoted to report the research activity in the field by means of a selection of scientific articles, where mathematical tools of the kinetic theory and swarms dynamics can contribute to modeling and simulations of living systems It focuses on a fascinating objective which cannot be tackled by the approach of the so-called hard sciences, mathematics without the invention of new mathematical theories. We mention with the aim of providing a fully detailed framework the kinetic theory approach developed by mean field and Fokker–Plank models [11], where a variety of interesting models mainly on social dynamics are reported and implemented by sharp numerical tools This editorial note is not limited to report about the contents, but it aims to develop a forward look to research perspectives somehow motivated by the contents of the issue. This topic is treated within a multiscale vision somehow inspired by the sixth Hilbert problem [12]
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