Naldi / Pareschi / Toscani Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences

1. Auflage 2010
ISBN: 978-0-8176-4946-3
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 438 Seiten

Reihe: Modeling and Simulation in Science, Engineering and Technology

Using examples from finance and modern warfare to the flocking of birds and the swarming of bacteria, the collected research in this volume demonstrates the common methodological approaches and tools for modeling and simulating collective behavior.The topics presented point toward new and challenging frontiers of applied mathematics, making the volume a useful reference text for applied mathematicians, physicists, biologists, and economists involved in the modeling of socio-economic systems.

Autoren/Hrsg.

Naldi, Giovanni

Pareschi, Lorenzo

Toscani, Giuseppe

Inhaltsverzeichnis

1;Preface;6
2;Contents;10
3;Economic modelling and financial markets;12
3.1;Agent-based models of economic interactions;13
3.1.1;1 Introduction;13
3.1.2;2 Order books;15
3.1.3;3 Wealth distributions;22
3.1.4;4 Minority games;28
3.1.5;5 Final remarks;33
3.1.6;6 Acknowledgements;34
3.1.7;References;34
3.2;On kinetic asset exchange models and beyond: microeconomic formulation, trade network, and all that;40
3.2.1;1 Introduction;40
3.2.2;2 Gas-like models;41
3.2.3;3 A microeconomic formulation;46
3.2.4;4 Models on directed networks;51
3.2.5;5 Preferential transactions and weighted trade network;55
3.2.6;6 Discussions and outlook;57
3.2.7;7 Acknowledgements;57
3.2.8;References;58
3.3;Microscopic and kinetic models in financial markets;60
3.3.1;1 Introduction;60
3.3.2;2 Microscopic models;61
3.3.3;3 Kinetic models;67
3.3.4;References;88
3.4;A mathematical theory for wealth distribution;90
3.4.1;1 Introduction;90
3.4.2;2 Kinetic wealth distribution models and mathematical tools;92
3.4.3;3 Results for the one-dimensional models;100
3.4.4;4 Results in the two-dimensional case;113
3.4.5;5 Conclusions;119
3.4.6;Acknowledgements;119
3.4.7;References;120
3.5;Tolstoy’s dream and the quest for statistical equilibrium in economics and the social sciences;123
3.5.1;1 Tolstoy’s dream;123
3.5.2;2 Statistical equilibrium in economics;124
3.5.3;3 An example: the taxation-redistribution game;127
3.5.4;Appendix: the P´olya distribution;134
3.5.5;References;141
4;Social modelling and opinion formation;142
4.1;New perspectives in the equilibrium statistical mechanics approach to social and economic sciences;143
4.1.1;1 Introduction;144
4.1.2;2 A brief introduction to many-body dynamics;145
4.1.3;3 Equilibrium behavior;149
4.1.4;4 Equilibrium statistical mechanics of the “ 2- body” model;151
4.1.5;5 Beyond detailed balance: diffusive strategic dynamics;165
4.1.6;6 Statics of many body interactions;168
4.1.7;7 A simple application to trading in markets;177
4.1.8;8 Conclusions and Outlooks;178
4.1.9;References;179
4.2;Kinetic modelling of complex socio- economic systems;181
4.2.1;1 Introduction;181
4.2.2;2 Some reasonings on the mathematical modelling of complex socio- economic systems;182
4.2.3;3 Mathematical tools;185
4.2.4;4 An example of application: competition for a secession under influence of media;192
4.2.5;5 Simulations;198
4.2.6;6 Conclusions;204
4.2.7;References;206
4.3;Mathematics and physics applications in sociodynamics simulation: the case of opinion formation and diffusion;208
4.3.1;1 Opinion dynamics;208
4.3.2;2 Binary opinion dynamics and beyond;213
4.3.3;3 Agents based model and discrete dynamical systems;218
4.3.4;4 The kinetic approach;220
4.3.5;5 New opportunities: an opinion;223
4.3.6;References;223
4.4;Global dynamics in adaptive models of collective choice with social influence;227
4.4.1;1 Introduction;227
4.4.2;2 Galam’s model;229
4.4.3;3 A mathematical formalization of Schelling model;231
4.4.4;4 The case of impulsive agents;238
4.4.5;5 A general model with different switching propensity;243
4.4.6;6 Conclusion;246
4.4.7;References;247
4.5;Modelling opinion formation by means of kinetic equations;249
4.5.1;1 Sociophysics;249
4.5.2;2 Kinetic approach in sociophysics: tools and methods;252
4.5.3;3 The main phenomenon: the compromise;256
4.5.4;4 Other sociological phenomena;264
4.5.5;5 Conclusion;270
4.5.6;References;271
5;Human behavior and swarming;275
5.1;On the modelling of vehicular traffic and crowds by kinetic theory of active particles;276
5.1.1;1 Introduction;276
5.1.2;2 Common features of vehicular traffic and crowds;278
5.1.3;3 Mathematical representation and structures;280
5.1.4;4 On the modelling of vehicular traffic;285
5.1.5;5 On the modelling of crowds;289
5.1.6;6 Critical analysis and perspectives;292
5.1.7;References;297
5.2;Particle, kinetic, and hydrodynamic models of swarming;300
5.2.1;1 Introduction;300
5.2.2;2 Particle models;302
5.2.3;3 Kinetic models;306
5.2.4;4 Hydrodynamic models;315
5.2.5;5 Variations on the theme;322
5.2.6;6 Numerical experiments;329
5.2.7;References;335
5.3;Modeling self-organization in pedestrians and animal groups from macroscopic and microscopic viewpoints;340
5.3.1;1 Self-organization in many-particle systems;340
5.3.2;2 Classical vs. intelligent particles;344
5.3.3;3 What mechanics for intelligent systems?;346
5.3.4;4 Mathematical modeling by time-evolving measures;348
5.3.5;5 Numerical results;356
5.3.6;6 Conclusions and research perspectives;363
5.3.7;Acknowledgements;364
5.3.8;References;364
5.4;Statistical physics and modern human warfare;368
5.4.1;1 Introduction;368
5.4.2;2 Two-population conflict model;370
5.4.3;3 Encounter fragmentation model;382
5.4.4;4 Outlook;391
5.4.5;Appendix: derivation of analytic solution for encounter fragmentation ( EF) model;392
5.4.6;References;398
5.5;Diffusive and nondiffusive population models;400
5.5.1;1 Introduction;400
5.5.2;2 Initial-value population models;401
5.5.3;3 Reaction–diffusion population models;403
5.5.4;4 Cross-diffusion population models;406
5.5.5;5 Structured population models;416
5.5.6;6 Time-delayed population models;420
5.5.7;References;421
6;Index;429