Modeling Complex Living Systems
A Kinetic Theory and Stochastic Game Approach
Published on 14. November 2007
Book
Hardback
XII, 220 pages
978-0-8176-4510-6 (ISBN)
Description
Thesubjectofthisbookisthemodelingofcomplex systemsinthelife sciences constituted by a large number of interacting entities called active particles. Their physical state includes, in addition to geometrical and mechanical variables, a variable called the activity, which characterizes the speci?c living system to be modeled. Interactions among particles not only modify the microscopic state, but may generate proliferative and/or destructive phenomena. The aim of the book is to develop mathematical methods and tools, even a new mathematics, for the modeling of living systems. The background idea is that the modeling of living systems requires technically complex mathematical methods, which may be s- stantially di?erent from those used to deal with inert matter. The?rstpart ofthe bookdiscussesmethodological issues, namely the derivation of various general mathematical frameworks suitable to model particular systems of interest in the applied sciences. The second part presents the various models and applications. The mathematical approach used in the book is based on mathema- cal kinetic theoryfor active particles, whichleads tothederivation of evo- tion equations for a one-particle distribution function over the microscopic state. Two types of equations, to be regarded as a general mathematical framework for deriving the models, are derived corresponding to short and long range interactions.
Reviews / Votes
"This nicely written book promotes the idea that the methods employed for modeling living systems may significantly differ from the techniques used for analyzing inert matter...This text, carefully written by a well-known expert, explains broad and profound applications of a new approach to modeling of nonlinear complex systems not only in the natural sciences, but also in systems describing social, ecological, and economic phenomena. It is a very useful reference for anyone interested in mathematical modeling of complex systems." (Svitlana P. Rogovchenko, Zentralblatt MATH )More details
Series
Edition
2008 ed.
Language
English
Place of publication
Boston
United States
Target group
Professional and scholarly
Research
Illustrations
37 s/w Abbildungen
XII, 220 p. 37 illus.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 18 mm
Weight
524 gr
ISBN-13
978-0-8176-4510-6 (9780817645106)
DOI
10.1007/978-0-8176-4600-4
Schweitzer Classification
Other editions
Additional editions
E-Book
10/2007
1st Edition
Birkhäuser
€96.29
Available for download
Person
Bouchra Aylaj is an Associate Professor with Habilitation in mathematics at University of Hassan II of Casablanca, Faculty Ain Chock, Morocco. She started her career in 2006 when she was called to develop a research program on mathematical modelling in biology. Her scientific activity has been focused on the following topics: scientific computing and control for risk analysis and analytical and computational problems in epidemiology. Subsequently, she moved her scientific interests to the modeling and related safety problems focused on social behaviors in human crowds.Nicola Bellomo is a distinguished professor at the University of Granada and Professor Emeritus at the Polytechnic University of Torino. He started his career in 1980 when he was called to cover the chair of mathematical physics and applied mathematics due to his scientific achievements on the mathematical theory of the Boltzmann equation and of stochastic differential equations. Subsequently, he moved his scientificinterests to the study of living systems, becoming one of the pioneers of the development of active particles methods to the modeling of large systems of self-propelled interacting entities. He is author of two books published by Birkhauser devoted to this topic. In 2009, he delivered the prestigious Shank Lecture on the modeling of immune competition, and was awarded the "Third Level Honor" in 2016 for scientific merits by the President of the Italian Republic.Livio Gibelli is a Lecturer in Mechanical Engineering at the University of Edinburgh. He received his Ph.D. in applied mathematics from the Politecnico di Milano and, prior to the current position, he worked as Research Fellow at the University of Warwick, Politecnico di Milano, Politecnico di Torino, and University of British Columbia. His main research interests include non-equilibrium multiphase fluid flows, the continuum description of slightly rarefied gases, the numerical methods for solving kinetic equations,and the modeling of crowd dynamics.Damian Knopoff is a chemical engineer and mathematician, holding a Ph.D. in Mathematics from Cordoba National University. Currently, he is an Associate Researcher at the Argentinian Scientific and Technical Research Council. His main research fields include nonlinear dynamical systems and numerical methods for differential equations with applications to the modeling and simulation of complex living systems, including biological phenomena, socio-economic systems, and crowd dynamics.
Content
From Scaling and Determinism to Kinetic Theory Representation.- Mathematical Structures of the Kinetic Theory for Active Particles.- Additional Mathematical Structures for Modeling Complex Systems.- Mathematical Frameworks.- Modeling of Social Dynamics and Economic Systems.- Mathematical Modeling.- Complex Biological Systems:.- Modeling Crowds and Swarms:Congested and Panic Flows.- Additional Concepts on the Modeling of Living Systems.