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

Front Cover
Springer Science & Business Media, Oct 5, 2007 - Mathematics - 220 pages
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.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

From Scaling and Determinism to Kinetic Theory Representation
1
12 Classical Models of Kinetic Theory
4
13 Discrete Velocity Models
13
14 Guidelines for Modeling Living Systems
15
15 Purpose and Plan of the Book
20
Mathematical Structures of the Kinetic Theory for Active Particles
27
22 The Generalized Distribution Function
29
23 Modeling Microscopic Interactions
35
55 Critical Analysis and Further Developments
104
Mathematical Modeling of Vehicular Traffic Flow Phenomena
109
62 Scaling and Representation
111
63 A Survey of Continuous Kinetic Traffic Models
121
64 Discrete Velocity Models
128
65 On the Model by Delitala and Tosin
134
66 On the Modeling by Active Particle Methods
144
Complex Biological Systems Mutations and Immune Competition
147

24 Mathematical Frameworks
44
25 Some Particular Frameworks
47
26 Additional Concepts
51
Additional Mathematical Structures for Modeling Complex Systems
53
32 Models with MixedType Interactions
54
33 Models with Exotic Proliferations
55
34 Phenomenological Frameworks
58
35 Open Systems
61
Mathematical Frameworks for Discrete Activity Systems
63
42 Motivations for a Discrete States Modeling
65
43 On the Discrete Distribution Function
66
44 Mathematical Framework
70
45 Additional Generalizations
74
46 Critical Analysis
79
Modeling of Social Dynamics and Economic Systems
81
52 A Model by Bertotti and Delitala
83
53 Qualitative Analysis and Simulations
89
54 Some Ideas on Further Modeling Perspectives
96
72 Modeling the Immune Competition
149
73 Mathematical Structures for Modeling
151
74 An Example of Mathematical Models
156
75 Modeling Developments and Perspectives
163
Modeling Crowds and Swarms Congested and Panic Flows
169
82 The Representation of Crowds and Swarms
172
83 Modeling by Macroscopic Equations
175
84 Modeling by Kinetic Theory Methods
179
85 Looking Forward
182
Additional Concepts on the Modeling of Living Systems
189
92 Mathematical Problems
191
93 Looking for New Mathematical Structures
196
94 Additional Issues on Modeling
199
95 Speculations on a Mathematical Theory for Living Systems
203
Collective Bibliography
209
Index
219
Copyright

Other editions - View all

Common terms and phrases

Popular passages

Page iii - USA wpaepmnas . epm . ornl . gov KR Rajagopal (Multiphase Flows) Department of Mechanical Engineering Texas A&M University College Station, TX 77843, USA KRaj agopaltaengr . tamu . edu Y.
Page 216 - Discrete velocity models of the Boltzmann equation: A survey on the mathematical aspects of the theory, SIAM Review, 30, 213-255, 1988.
Page iii - Advisory Editorial Board M.Avellaneda (Modeling in Economics) Courant Institute of Mathematical Sciences New York University 251 Mercer Street New York, NY 1001 2, USA...
Page 216 - Prigogine, I. and Herman, R. (1971) Kinetic Theory of Vehicular Traffic. Elsevier, New York.
Page 214 - Biol., 37 (1998), 235-252. [JAa] JAGER E. and SEGEL L., On the distribution of dominance in a population of interacting anonymous organisms, SIAM J. Appl. Math., 52 (1992), 1442-1468. [LAa] LACHOWICZ M., A system of stochastic differential equations modeling Euler and Navier Stokes hydrodynamic equations, Japan J.
Page 215 - Koch, AJ and Meinhardt, H. (1994) Biological pattern formation: from basic mechanisms to complex structures.
Page iii - Mathematiques pour ('lndustrie et la Physique Universite P. Sabatier Toulouse 3 118RoutedeNarbonne 31062 Toulouse Cedex, France degondOmip . ups-tlse . fr A. Deutsch (Complex Systems in the Life Sciences) Center for lnformation Services and High Performance Computing Technische Universita't Dresden 01062 Dresden, Germany andreas...

Bibliographic information