Dynamical Systems

In this Chapter, we provide the definitions, notions and examples relevant for the analysis of the dynamical systems of interest to us in the remainder of this book. We start with with a description of dynamical systems and we provide a taxonomy. Then, we define continuous-time dynamical systems either in the form of ordinary differential equations (ODE) or from systems of ODE. Afterwards, we introduce the general concept of stability and of stable limit cycles and periodicity. That is followed by the notion of properties such as attractors and repellers. The basis of existence of periodic orbits in continuous-time systems and 1-d maps, is obtained in the last Section.