Modeling Complex Systems / Edition 2

by Nino Boccara

Overview

The essential points of this first chapter are • The definition of a complex system • The notion of emergence • The definition 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 first section is devoted to the description of these properties. To interpret the time evolution of a system, scientists build up models, which are simplified 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, of the state of the system. There exist different types of dynamical systems. Some of them are defined in the third section. 1 There is an extensive literature on mathematical modeling. The reader may, for example, consult [11,88,163,233].

Product Details

ISBN-13:	9781461426813
Publisher:	Springer New York
Publication date:	11/05/2012
Series:	Graduate Texts in Physics
Edition description:	Softcover reprint of hardcover 2nd ed. 2010
Pages:	490
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

About the Author

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.

Table of Contents

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

Editorial Reviews

From the reviews of the second edition:

“Boccara’s approach is firmly based on dynamical systems theory, differential equations, and maps, with a very solid mathematical treatment, cast at times in terms of definitions and theorems. … The book is very well suited for graduate or advanced undergraduate studies and comes with a problem and solution section at the end of every chapter. … The book covers in any case a plethora of models and is highly recommendable for everybody wishing to attain a good knowledge of classical complex system theory.”­­­ (Claudius Gros, SIAM Review, Vol. 53 (4), 2011)

From the Publisher