Modeling Complex Systems (2^nd Ed., 2nd ed. 2010) Graduate Texts in Physics Series

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].

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

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.

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