Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences (eBook)

Giovanni Naldi, Lorenzo Pareschi, Giuseppe Toscani (Herausgeber)

eBook Download: PDF

2010 | 2010
X, 438 Seiten
Birkhauser Boston (Verlag)
978-0-8176-4946-3 (ISBN)

Infos

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.

---

Mathematical modeling using dynamical systems and partial differential equations is now playing an increasing role in the understanding of complex multi-scale phenomena. Behavior in seemingly different areas such as sociology, economics, and the life sciences can be described by closely related models. Using examples from financial markets 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.

Inhalt

Preface 6
Contents 10
Economic modelling and financial markets 12
Agent-based models of economic interactions 13
1 Introduction 13
2 Order books 15
3 Wealth distributions 22
4 Minority games 28
5 Final remarks 33
6 Acknowledgements 34
References 34
On kinetic asset exchange models and beyond: microeconomic formulation, trade network, and all that 40
1 Introduction 40
2 Gas-like models 41
3 A microeconomic formulation 46
4 Models on directed networks 51
5 Preferential transactions and weighted trade network 55
6 Discussions and outlook 57
7 Acknowledgements 57
References 58
Microscopic and kinetic models in financial markets 60
1 Introduction 60
2 Microscopic models 61
3 Kinetic models 67
References 88
A mathematical theory for wealth distribution 90
1 Introduction 90
2 Kinetic wealth distribution models and mathematical tools 92
3 Results for the one-dimensional models 100
4 Results in the two-dimensional case 113
5 Conclusions 119
Acknowledgements 119
References 120
Tolstoy’s dream and the quest for statistical equilibrium in economics and the social sciences 123
1 Tolstoy’s dream 123
2 Statistical equilibrium in economics 124
3 An example: the taxation-redistribution game 127
Appendix: the P´olya distribution 134
References 141
Social modelling and opinion formation 142
New perspectives in the equilibrium statistical mechanics approach to social and economic sciences 143
1 Introduction 144
2 A brief introduction to many-body dynamics 145
3 Equilibrium behavior 149
4 Equilibrium statistical mechanics of the “ 2- body” model 151
5 Beyond detailed balance: diffusive strategic dynamics 165
6 Statics of many body interactions 168
7 A simple application to trading in markets 177
8 Conclusions and Outlooks 178
References 179
Kinetic modelling of complex socio- economic systems 181
1 Introduction 181
2 Some reasonings on the mathematical modelling of complex socio- economic systems 182
3 Mathematical tools 185
4 An example of application: competition for a secession under influence of media 192
5 Simulations 198
6 Conclusions 204
References 206
Mathematics and physics applications in sociodynamics simulation: the case of opinion formation and diffusion 208
1 Opinion dynamics 208
2 Binary opinion dynamics and beyond 213
3 Agents based model and discrete dynamical systems 218
4 The kinetic approach 220
5 New opportunities: an opinion 223
References 223
Global dynamics in adaptive models of collective choice with social influence 227
1 Introduction 227
2 Galam’s model 229
3 A mathematical formalization of Schelling model 231
4 The case of impulsive agents 238
5 A general model with different switching propensity 243
6 Conclusion 246
References 247
Modelling opinion formation by means of kinetic equations 249
1 Sociophysics 249
2 Kinetic approach in sociophysics: tools and methods 252
3 The main phenomenon: the compromise 256
4 Other sociological phenomena 264
5 Conclusion 270
References 271
Human behavior and swarming 275
On the modelling of vehicular traffic and crowds by kinetic theory of active particles 276
1 Introduction 276
2 Common features of vehicular traffic and crowds 278
3 Mathematical representation and structures 280
4 On the modelling of vehicular traffic 285
5 On the modelling of crowds 289
6 Critical analysis and perspectives 292
References 297
Particle, kinetic, and hydrodynamic models of swarming 300
1 Introduction 300
2 Particle models 302
3 Kinetic models 306
4 Hydrodynamic models 315
5 Variations on the theme 322
6 Numerical experiments 329
References 335
Modeling self-organization in pedestrians and animal groups from macroscopic and microscopic viewpoints 340
1 Self-organization in many-particle systems 340
2 Classical vs. intelligent particles 344
3 What mechanics for intelligent systems? 346
4 Mathematical modeling by time-evolving measures 348
5 Numerical results 356
6 Conclusions and research perspectives 363
Acknowledgements 364
References 364
Statistical physics and modern human warfare 368
1 Introduction 368
2 Two-population conflict model 370
3 Encounter fragmentation model 382
4 Outlook 391
Appendix: derivation of analytic solution for encounter fragmentation ( EF) model 392
References 398
Diffusive and nondiffusive population models 400
1 Introduction 400
2 Initial-value population models 401
3 Reaction–diffusion population models 403
4 Cross-diffusion population models 406
5 Structured population models 416
6 Time-delayed population models 420
References 421
Index 429

Produkt-Details

• Erscheint lt. Verlag: 12.8.2010
• Reihe/Serie: Modeling and Simulation in Science, Engineering and Technology
• Reihe/Serie: Modeling and Simulation in Science, Engineering and Technology
• Zusatzinfo: X, 438 p. 98 illus.
• Verlagsort: Boston
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften ► Biologie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Thermodynamik
• Themenwelt: Recht / Steuern ► Wirtschaftsrecht
• Themenwelt: Technik
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management
• Schlagworte: collective behavior • kinetic modeling • Mathematics • Multi-scale modeling • Nonlinear analysis • partial differential equation • Partial differential equations • population dynamics • Quantitative Finance • socio-economic systems • Statistica
• ISBN-10: 0-8176-4946-8 / 0817649468
• ISBN-13: 978-0-8176-4946-3 / 9780817649463