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

Preface     xi
From Scaling and Determinism to Kinetic Theory Representation     1
Scaling and Determinism     1
Classical Models of Kinetic Theory     4
Discrete Velocity Models     13
Guidelines for Modeling Living Systems     15
Purpose and Plan of the Book     20
Mathematical Structures of the Kinetic Theory for Active Particles     27
Introduction     27
The Generalized Distribution Function     29
Modeling Microscopic Interactions     35
Mathematical Frameworks     44
Some Particular Frameworks     47
Additional Concepts     51
Additional Mathematical Structures for Modeling Complex Systems     53
Introduction     53
Models with Mixed-Type Interactions     54
Models with Exotic Proliferations     55
Phenomenological Frameworks     58
Open Systems     61
Mathematical Frameworks for Discrete Activity Systems     63
Introduction     63
Motivations for a Discrete States Modeling     65
On the Discrete Distribution Function     66
Mathematical Framework     70
Additional Generalizations     74
Critical Analysis     79
Modeling of Social Dynamics and Economic Systems     81
Introduction     81
A Model by Bertotti and Delitala     83
Qualitative Analysis and Simulations     89
Some Ideas on Further Modeling Perspectives     96
Critical Analysis and Further Developments     104
Mathematical Modeling of Vehicular Traffic Flow Phenomena     109
Introduction     109
Scaling and Representation     111
A Survey of Continuous Kinetic Traffic Models     121
Discrete Velocity Models     128
On the Model by Delitala and Tosin     134
On the Modeling by Active Particle Methods     144
Complex Biological Systems: Mutations and Immune Competition     147
Introduction     147
Modeling the Immune Competition     149
Mathematical Structures for Modeling     151
An Example of Mathematical Models     156
Modeling Developments and Perspectives     163
Modeling Crowds and Swarms: Congested and Panic Flows     169
Introduction     169
The Representation of Crowds and Swarms     172
Modeling by Macroscopic Equations      175
Modeling by Kinetic Theory Methods     179
Looking Forward     182
Additional Concepts on the Modeling of Living Systems     189
Introduction     189
Mathematical Problems     191
Looking for New Mathematical Structures     196
Additional Issues on Modeling     199
Speculations on a Mathematical Theory for Living Systems     203
Collective Bibliography     209
Index     219