Modeling Complex Living Systems
Bellomo, Nicola.
creator
author.
SpringerLink (Online service)
text
xxu
2008
monographic
eng
access
XII, 220 p. 37 illus. online resource.
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 toolsâ€”hopefully a "new" mathematicsâ€”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 Living Systems 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.
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.
by Nicola Bellomo.
Mathematics
Applied mathematics
Engineering mathematics
Game theory
Mathematical models
Biomathematics
Physics
Mathematics
Mathematical Modeling and Industrial Mathematics
Applications of Mathematics
Mathematical and Computational Biology
Game Theory, Economics, Social and Behav. Sciences
Mathematical Methods in Physics
Appl.Mathematics/Computational Methods of Engineering
TA342-343
003.3
Springer eBooks
Modeling and Simulation in Science, Engineering and Technology
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http://dx.doi.org/10.1007/978-0-8176-4600-4
http://dx.doi.org/10.1007/978-0-8176-4600-4
100301
20180115171436.0
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