Modeling Complex Systems PDF

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].