| 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. |