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

1. Front Matter

   Pages i-x

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2. Economic modelling and financial markets

   1. Front Matter

      Pages 1-1

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   2. Agent-based models of economic interactions

      • Anirban Chakraborti, Guido Germano

      Pages 3-29

   3. On kinetic asset exchange models and beyond: microeconomic formulation,trade network, and all that

      • Arnab Chattejee

      Pages 31-50

   4. Microscopic and kinetic models in financial markets

      • Stephane Cordier, Dario Maldarella, Lorenzo Pareschi, Cyrille Piatecki

      Pages 51-80

   5. A mathematical theory for wealth distribution

      • Bertram Düring, Daniel Matthes

      Pages 81-113

   6. Tolstoy’s dream and the quest for statistical equilibrium in economics and the social sciences

      • Ubaldo Garibaldi, Enrico Scalas

      Pages 115-133

3. Social modelling and opinion formation

   1. Front Matter

      Pages 135-135

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   2. New perspectives in the equilibrium statistical mechanics approach to social and economic sciences

      • Elena Agliari, Adriano Barra, Raffaella Burioni, Pierluigi Contucci

      Pages 137-174

   3. Kinetic modelling of complex socio-economic systems

      • Giulia Ajmone Marsan

      Pages 175-201

   4. Mathematics and physics applications in sociodynamics simulation: the case of opinion formation and diffusion

      • Giacomo Aletti, Ahmad K. Naimzada, Giovanni Naldi

      Pages 203-221

   5. Global dynamics in adaptive models of collective choice with social influence

      • Gian-Italo Bischi, Ugo Merlone

      Pages 223-244

   6. Modelling opinion formation by means of kinetic equations

      • Laurent Boudin, Francesco Salvarani

      Pages 245-270

4. Human behavior and swarming

   1. Front Matter

      Pages 271-271

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   2. On the modelling of vehicular traffic and crowds by kinetic theory of active particles

      • Nicola Bellomo, Abdelghani Bellouquid

      Pages 273-296

   3. Particle, kinetic, and hydrodynamic models of swarming

      • José A. Carrillo, Massimo Fornasier, Giuseppe Toscani, Francesco Vecil

      Pages 297-336

   4. Modeling self-organization in pedestrians and animal groups from macroscopic and microscopic viewpoints

      • Emiliano Cristiani, Benedetto Piccoli, Andrea Tosin

      Pages 337-364

   5. Statistical physics and modern human warfare

      • Alex Dixon, Zhenyuan Zhao, Juan Camilo Bohorquez, Russell Denney, Neil Johnson

      Pages 365-396

   6. Diffusive and nondiffusive population models

      • Ansgar Jüngel

      Pages 397-425

5. Back Matter

   Pages 427-435

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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.

• STATISTICA
• collective behavior
• kinetic modeling
• mathematics
• multi-scale modeling
• nonlinear analysis
• partial differential equation
• population dynamics
• socio-economic systems
• partial differential equations
• quantitative finance

• Dipartimento di Matematica, Università di Milano, Milano, Italy

  Giovanni Naldi

• Dipartimento di Matematica, Università di Ferrara, Ferrara, Italy

  Lorenzo Pareschi

• Dipartimento di Matematica, Università di Pavia, Pavia, Italy

  Giuseppe Toscani

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