When a system becomes unstable or noise becomes excessive, often regulations of the form of limiters (barriers obstructing excursion into undesired areas of the phase space) are imposed. It is hoped that by the influence of this element, the system can be calmed and its behaviour can be...

Many dynamical systems depend on parameters. One may expect that small variations of the parameters produce no significant changes in the orbits. As was shown in Chap. 3 for the Logistic Map, even in simple cases, there exist critical values such that, moving the parameters through them, the...

In this chapter, we first precise the concept of dynamical systems, and then we introduce the concept of chaos, which is characterized by a sensitive dependence on initial conditions. To quantify this, dynamical (Lyapunov exponents) and probabilistic (dimensions) measures are introduced.

In this chapter, we introduce the concept of the embedding dimension, as the smallest topological dimension required to ensure that an object described by simpler (often scalar) time series can be embedded in a higher topological dimension.