Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences (Modeling and Simulation in Science, Engineering and Technology)

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. Systems made out of a large enough number of individual members can be said to exhibit a collective behavior, from which insight can be gathered in a way that real-life experiments cannot. 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. Specific topics covered include: \* analysis of wealth distributions \* dynamics of price formation \* spreading of opinions \* models of social behavior \* population dynamics \* aggregation and swarming 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. Front Matter....Pages i-x Front Matter....Pages 1-1 Agent-based models of economic interactions....Pages 3-29 On kinetic asset exchange models and beyond: microeconomic formulation,trade network, and all that....Pages 31-50 Microscopic and kinetic models in financial markets....Pages 51-80 A mathematical theory for wealth distribution....Pages 81-113 Tolstoy’s dream and the quest for statistical equilibrium in economics and the social sciences....Pages 115-133 Front Matter....Pages 135-135 New perspectives in the equilibrium statistical mechanics approach to social and economic sciences....Pages 137-174 Kinetic modelling of complex socio-economic systems....Pages 175-201 Mathematics and physics applications in sociodynamics simulation: the case of opinion formation and diffusion....Pages 203-221 Global dynamics in adaptive models of collective choice with social influence....Pages 223-244 Modelling opinion formation by means of kinetic equations....Pages 245-270 Front Matter....Pages 271-271 On the modelling of vehicular traffic and crowds by kinetic theory of active particles....Pages 273-296 Particle, kinetic, and hydrodynamic models of swarming....Pages 297-336 Modeling self-organization in pedestrians and animal groups from macroscopic and microscopic viewpoints....Pages 337-364 Statistical physics and modern human warfare....Pages 365-396 Diffusive and nondiffusive population models....Pages 397-425 Back Matter....Pages 427-435 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. Systems made out of a large enough number of individual members can be said to exhibit a collective behavior, from which insight can be gathered in a way that real life experiments cannot. 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. Specific topics covered include: analysis of wealth distributions, dynamics of price formation, spreading of opinions, models of social behavior, population dynamics, and aggregation and swarming. 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. Using examples from financial markets and modern warfare to the flocking of birds and the swarming of bacteria, this book shows how behavior in such diverse areas as sociology, economics, and the life sciences can be described by closely related models.