Interacting Multiagent Systems: Kinetic equations and Monte Carlo methods

Hardcover | December 28, 2013

byLorenzo Pareschi, Giuseppe Toscani

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The description of emerging collective phenomena and self-organization in systems composed of large numbers of individuals has gained increasing interest from various research communities in biology, ecology, robotics and control theory, as well as sociology and economics.Applied mathematics is concerned with the construction, analysis and interpretation of mathematical models that can shed light on significant problems of the natural sciences as well as our daily lives. To this set of problems belongs the description of the collective behaviours of complex systemscomposed by a large enough number of individuals. Examples of such systems are interacting agents in a financial market, potential voters during political elections, or groups of animals with a tendency to flock or herd. Among other possible approaches, this book provides a step-by-step introductionto the mathematical modelling based on a mesoscopic description and the construction of efficient simulation algorithms by Monte Carlo methods. The arguments of the book cover various applications, from the analysis of wealth distributions, the formation of opinions and choices, the price dynamics in a financial market, to the description of cell mutations and the swarming of birds and fishes. By means of methods inspired by the kinetictheory of rarefied gases, a robust approach to mathematical modelling and numerical simulation of multi-agent systems is presented in detail. The content is a useful reference text for applied mathematicians, physicists, biologists and economists who want to learn about modelling and approximationof such challenging phenomena.

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From the Publisher

The description of emerging collective phenomena and self-organization in systems composed of large numbers of individuals has gained increasing interest from various research communities in biology, ecology, robotics and control theory, as well as sociology and economics.Applied mathematics is concerned with the construction, analysis...

Lorenzo Pareschi is full professor of numerical analysis at the University of Ferrara. He holds a PhD in mathematics from Bologna University (1996). He is a leading expert in computational methods and modelling for nonlinear partial differential equations. His research interests include kinetic equations, hyperbolic conservation laws ...
Format:HardcoverDimensions:392 pages, 9.69 × 6.73 × 0.98 inPublished:December 28, 2013Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199655464

ISBN - 13:9780199655465

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Table of Contents

Part I: Kinetic Modelling and Simulation1. A short introduction to kinetic equations2. Mathematical tools3. Monte Carlo strategies4. Monte Carlo methods for kinetic equationsPart II: Multiagent Kinetic Equations5. Models for wealth distribution6. Opinion modelling and consensus formation7. A further insight into economy and social sciences8. Modelling in life sciencesAppendix A: Basic arguments on Fourier transformsAppendix B: Important probability distributions

Editorial Reviews

"The area of research on complex, multi-agent systems has gained a lot of momentum recently, and is expanding rapidly. This self-contained book opens the door to this novel field for interested graduate students and researchers. It is based on a solid mathematical foundation and takes itsreader on an exciting journey, from the early ideas of Boltzmann and Maxwell to the forefront of today's research." --Bertram During, University of Sussex