Graduate Texts in Physics

Boccara, Nino

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].

Details

Published by: Springer

Publication Date: 2010-09-21

Format: Hardcover

ISBN-13: 9781441965615

DOI: 10.1007/978-1-4419-6562-2

Dimensions: 235cm x155cm

Pages: 490