Numerical Tools

Abstract

The theoretical results presented above allow to establish the existence of chaotic trajectories in several dynamical systems, which fulfill the assumptions of the appropriate theorems. For example, when the difference equation is unimodal, it is possible to apply the Li/Yorke theorem or Sarkovskii’s theorem and to establish the existence of chaos (defined in the sense of one of the definitions provided in the previous chapters). However, in many cases it may be difficult or analytically impossible to detect a period-three cycle, and for most differential equation systems there are no theoretical results at all. Experiments show that even for cycles of a relatively low period it may be impossible to distinguish regular time series from completely chaotic series by simple visual inspection.