期刊
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
卷 23, 期 10, 页码 1861-1913出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S021820251350053X
关键词
Living systems; collective behavior; self-organization; nonlinear interactions; learning; large deviations
资金
- Ministerio de Ciencia e Innovacion (Spain) [MTM2011-23384]
- Junta de Andalucia [P08-FQM-4267]
- MIUR
- Italian Minister of University and Research
- PRIN Grant
This paper presents a revisiting, with developments, of the so-called kinetic theory for active particles, with the main focus on the modeling of nonlinearly additive interactions. The approach is based on a suitable generalization of methods of kinetic theory, where interactions are depicted by stochastic games. The basic idea consists in looking for a general mathematical structure suitable to capture the main features of living, hence complex, systems. Hopefully, this structure is a candidate towards the challenging objective of designing a mathematical theory of living systems. These topics are treated in the first part of the paper, while the second one applies it to specific case studies, namely to the modeling of crowd dynamics and of the immune competition.
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