Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences - Naldi, Giovanni; Pareschi, Lorenzo; Toscani, Giuseppe; SpringerLink (Online service) (Boston : Birkhäuser Boston, 2010)
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.
Economic modelling and financial markets -- Agent-based models of economic interactions -- On kinetic asset exchange models and beyond: microeconomic formulation,trade network, and all that -- Microscopic and kinetic models in financial markets -- A mathematical theory for wealth distribution -- Tolstoy's dream and the quest for statistical equilibrium in economics and the social sciences -- Social modelling and opinion formation -- New perspectives in the equilibrium statistical mechanics approach to social and economic sciences -- Kinetic modelling of complex socio-economic systems -- Mathematics and physics applications in sociodynamics simulation: the case of opinion formation and diffusion -- Global dynamics in adaptive models of collective choice with social influence -- Modelling opinion formation by means of kinetic equations -- Human behavior and swarming -- On the modelling of vehicular traffic and crowds by kinetic theory of active particles -- Particle, kinetic, and hydrodynamic models of swarming -- Modeling self-organization in pedestrians and animal groups from macroscopic and microscopic viewpoints -- Statistical physics and modern human warfare -- Diffusive and nondiffusive population models.
Keywords: MATHEMATICS; DIFFERENTIAL EQUATIONS, PARTIAL; BIOLOGY -- MATHEMATICS; FINANCE; ECONOMICS, MATHEMATICAL; MATHEMATICS; MATHEMATICAL MODELING AND INDUSTRIAL MATHEMATICS; STATISTICAL PHYSICS, DYNAMICAL SYSTEMS AND COMPLEXITY; PARTIAL DIFFERENTIAL EQUATIONS; MATHEMATICAL BIOLOGY IN GENERAL; QUANTITATIVE FINANCE; GAME THEORY/MATHEMATICAL METHODS