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Modeling Complex Living SystemsAdditional Concepts on the Modeling of Living Systems

Modeling Complex Living Systems: Additional Concepts on the Modeling of Living Systems Additional Concepts on the Modeling of Living Systems 9.1 Introduction The preceding chapters were devoted to the development and applica- tion of the methods of the mathematical kinetic theory for active particles to the modeling of large living systems of interacting entities. The term active particles has been used to denote entities whose mi- croscopic state includes, in addition to geometrical and mechanical variables (classically position and velocity), a further variable, called activity,which represents the ability of the interacting particles to organize their behavior according to individual strategies typical of the system under consideration. Interactions modify the whole microscopic state by a dynamics, where laws of classical mechanics can be modified by the presence of the activity vari- able. The overall state of the system is described by the probability distribu- tion function over the microscopic state, while the macroscopic description is obtained by weighted moments of the distribution function. A detailed analysis of microscopic interactions and of the strategies developed by the active particles leads, using technical calculations, to an evolution equation (the model) for the distribution function. The contents of the preceding chapters can be divided into two parts. The first one was devoted to the methodological http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Modeling Complex Living SystemsAdditional Concepts on the Modeling of Living Systems

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Publisher
Birkhäuser Boston
Copyright
© Birkhäuser Boston 2008
ISBN
978-0-8176-4510-6
Pages
189 –207
DOI
10.1007/978-0-8176-4600-4_9
Publisher site
See Chapter on Publisher Site

Abstract

Additional Concepts on the Modeling of Living Systems 9.1 Introduction The preceding chapters were devoted to the development and applica- tion of the methods of the mathematical kinetic theory for active particles to the modeling of large living systems of interacting entities. The term active particles has been used to denote entities whose mi- croscopic state includes, in addition to geometrical and mechanical variables (classically position and velocity), a further variable, called activity,which represents the ability of the interacting particles to organize their behavior according to individual strategies typical of the system under consideration. Interactions modify the whole microscopic state by a dynamics, where laws of classical mechanics can be modified by the presence of the activity vari- able. The overall state of the system is described by the probability distribu- tion function over the microscopic state, while the macroscopic description is obtained by weighted moments of the distribution function. A detailed analysis of microscopic interactions and of the strategies developed by the active particles leads, using technical calculations, to an evolution equation (the model) for the distribution function. The contents of the preceding chapters can be divided into two parts. The first one was devoted to the methodological

Published: Jan 1, 2008

Keywords: Kinetic Theory; Living System; Mathematical Structure; Active Particle; Social Dynamic

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