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Modeling Complex Systems

  • Textbook
  • © 2004

Overview

Part of the book series: Graduate Texts in Contemporary Physics (GTCP)

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Table of contents (8 chapters)

  1. Introduction

  2. Mean-Field Type Models

  3. Agent-Based Models

Keywords

About this book

The preface is that part of a book which is written last, placed ?rst, and read least. Alfred J. Lotka Elements of Physical Biology Baltimore: Williams & Wilkins Company 1925 The purpose of this book is to show how models of complex systems are built up and to provide the mathematical tools indispensable for studying their dynamics. This is not, however, a book on the theory of dynamical systems illustrated with some applications; the focus is on modeling, so, in prese- ing the essential results of dynamical system theory, technical proofs of th- rems are omitted, but references for the interested reader are indicated. While mathematical results on dynamical systems such as di?erential equations or recurrence equations abound, this is far from being the case for spatially - tendedsystemssuchasautomatanetworks,whosetheoryisstillinitsinfancy. Many illustrative examples taken from a variety of disciplines, ranging from ecology and epidemiology to sociology and seismology, are given. This is an introductory text directed mainly to advanced undergraduate students in most scienti?c disciplines, but it could also serve as a reference book for graduate students and young researchers. The material has been ´ taught to junior students at the Ecole de Physique et de Chimie in Paris and the University of Illinois at Chicago. It assumes that the reader has certain fundamental mathematical skills, such as calculus.

Reviews

From the reviews of the first edition:

JOURNAL OF PHYSICS A: MATHEMATICAL AND GENERAL

Review by M Schreckenberg, Fachbereich Physik, Duisburg-Essen University, Germany

"This book by Nino Boccara presents a compilation of model systems commonly termed as `complex'. It starts with a definition of the systems under consideration and how to build up a model to describe the complex dynamics. The subsequent chapters are devoted to various categories of mean-field type models (differential and recurrence equations, chaos) and of agent-based models (cellular automata, networks and power-law distributions). Each chapter is supplemented by a number of exercises and their solutions. … The book is written as a textbook for interested students as well as serving as a comprehensive reference for experts. It is an ideal source for topics to be presented in a lecture on dynamics of complex systems. This is the first book on this `wide' topic and I have long awaited such a book. … In my opinion this is one of the best textbooks published during the last decade and even experts can learn a lot from it."

"Boccara has written a self-contained textbook that covers topics from basic nonlinear mathematics to agent-based models for systems with spatiotemporal emergent behavior. His book is clearly written … illustrated and full of examples and good problems. … This book is a welcome addition to the field and would make an excellent textbook for advanced undergraduates. I would also recommend it to those wanting to learn about nonlinear and complex systems. … Boccara’s book is an excellent place to start to become acquainted with complex systems." (Michael F. Shlesinger, Journal of Statistical Physics, Vol. 119 (3-4), May, 2005)

"This is an important book, of pedagogical use to a cohort of upcoming students and as an overview of the mathematical techniques currently available to the complex system manager. Your reviewer greatly enjoyedreading it and found much in it that was new and interesting and readily understandable." (Dr. D. J. Jefferies, Contemporary Physics, Vol. 46 (1), 2005)

"Boccara’s Modeling Complex Systems is full of useful knowledge … . Every chapter contains a remarkable number of examples that mix classical and up-to-date models … . The ideal audience for Boccara’s book is first- or second-year physics graduate students who have had a one-semester course in modern statistical mechanics … . Readers so prepared will find the book clear and well worth reading. Modern Complex Systems should be the standard introductory textbook to the physics of complex systems for the foreseeable future." (Cosma Shalizi, Physics Today, February, 2005)

"This nice book can serve as an introduction to modeling complex systems, but it can also be used both as a general presentation and as a reference book for anyone wanting to find in a single book on complex systems simultaneously models, modeling tools, examples, theoretical results and interesting applications. … Each chapter ends with exercises (and solutions). The book ends with a bibliography of more than 350 items, adding to its very good quality." (Jean-Paul Allouche, Zentralblatt MATH, Vol. 1072, 2005)

Authors and Affiliations

  • Department of Physics, University of Illinois-Chicago, Chicago, USA

    Nino Boccara

Bibliographic Information

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