Modeling Complex Living Systems: A Kinetic Theory and Stochastic Game Approach - Rilegato

Bellomo, Nicola

Rilegato

ISBN 10: 0817645101 ISBN 13: 9780817645106

Casa editrice: Springer Basel AG, 2007

Riassunto

The aim of the book is to develop mathematical methods and tools, even a new mathematics, for the modeling of living systems. The?rstpart ofthe bookdiscussesmethodological issues, namely the derivation of various general mathematical frameworks suitable to model particular systems of interest in the applied sciences.

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Using tools from mathematical kinetic theory and stochastic game theory, this work deals with the modeling of large complex systems in the applied sciences, particularly those comprised of several interacting individuals whose dynamics follow rules determined by some organized, or even "intelligent" ability. Traditionally, methods of mathematical kinetic theory have been applied to model the evolution of large systems of interacting classical or quantum particles. This book, on the other hand, examines the modeling of living systems as opposed to inert systems.

The author develops new mathematical methods and tools―hopefully a "new" mathematics―toward the modeling of living systems. Such tools need to be far more complex than those dealing with systems of inert matter. The first part of the book deals with deriving general evolution equations that can be customized to particular systems of interest in the applied sciences. The second part of the book deals with various models and applications.

The presentation unfolds using the following common approach in each chapter:

* Phenomenological interpretation of the physical system in the context of mathematical modeling

* Derivation of the mathematical model using methods from mathematical kinetic theory for active particles

* Simulations, parameter sensitivity analysis, and critical inspection of the derived model towards validation

* Overview of presented ideas to improve existing models, with special emphasis on applications

Specific topics covered include:

* Modeling of the competition between cells of an aggressive invasive agent and cells of the immune system

* Modeling of vehicular traffic flow

* Modeling of swarms and crowd dynamics in complex geometric environments

* Methodological aspects related to multiscale modeling of large systems viewed as interconnected subsystems

Modeling Complex LivingSystems is a valuable resource for applied mathematicians, engineers, physicists, biologists, economists, and graduate students involved in modeling complex social systems and living matter in general.

Dettagli dell'edizione

• Editore: Springer Basel AG
• Data di pubblicazione: 2007
• Lingua: Inglese
• ISBN 10: 0817645101
• ISBN 13: 9780817645106
• Rilegatura: Copertina rigida
• Numero di pagine: 236
• Contatto del produttore: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Germania