| 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. There is no precise
definition of complex systems. Most authors, however, 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 dynamical
systems. A dynamical system is essentially a set of equations whose solution
describes the evolution, as a function of time, of the state of the system. There
exist different types of dynamical systems. Some of them are defined in the
third section. |
