Modeling Complex Systems

This book illustrates how models of complex systems are built up and provides indispensable mathematical tools for studying their dynamics. This second edition includes more recent research results and many new and improved worked out examples and exercises.

The essential points of this ?rst chapter are • The de?nition of a complex system • The notion of emergence • The de?nition of a model • The notion of dynamical system This book is about the dynamics of complex systems. Roughly speaking, a system is a collection of interacting elements making up a whole such as, for instance, a mechanical clock. While many systems may be quite complicated, they are not necessarily considered to be complex. Today, most authors agree on the essential properties a system has to possess to be called complex. The ?rst section is devoted to the description of these properties. To interpret the time evolution of a system, scientists build up models, which are simpli?ed mathematical representations of the system. The exact purpose of a model and what its essential features should be is explained in the second section. The mathematical models that will be discussed in this book are dynami- 1 calsystems. A dynamical system is essentially a set of equations whose- lutiondescribesthe evolution,asafunction oftime, ofthe state ofthe system. There exist di?erent types of dynamical systems. Some of them are de?ned in the third section. 1 There is an extensive literature on mathematical modeling. The reader may, for example, consult [11,88,163,233].

Explores the process of modeling complex systems in the widest sense, drawing on many examples from diverse fields Presents new results recently obtained in the field of modeling complex systems Contains new worked examples and exercises whose complete solutions are given Includes supplementary material: sn.pub/extras

Autorentext
Dr. Nino Boccara is Professor Emeritus of Physics at the University of Illinois at Chicago, Professor Emeritus of Mathematics at the Ecole Supérieure de Physique et Chimie de la Ville de Paris, and Former Director of Research in Theoretical Physics at the CNRS.

Klappentext

Modeling Complex Systems, 2nd Edition, explores the process of modeling complex systems, providing examples from such diverse fields as ecology, epidemiology, sociology, seismology, and economics. It illustrates how models of complex systems are built and provides indispensable mathematical tools for studying their dynamics.

This vital introductory text is useful for advanced undergraduate students in various scientific disciplines, and serves as an important reference book for graduate students and young researchers.

This enhanced second edition includes: .

-recent research results and bibliographic references

-extra footnotes which provide biographical information on cited scientists who have made significant contributions to the field

-new and improved worked-out examples to aid a student's comprehension of the content

-exercises to challenge the reader and complement the material

Nino Boccara is also the author of Essentials ofMathematica: With Applications to Mathematics and Physics (Springer, 2007).

Inhalt
How to Build Up a Model.- Differential Equations.- Recurrence Equations.- Chaos.- Spatial Models.- Networks.- Power-Law Distributions.