Investigating Dynamics by Symbolic Analysis: Tunings for an Efficient Computation of the Symbolic Image

Numerical methods based on the conceptual framework of symbolic analysis are important tools for the study of non-linear dynamical systems. Implementations of these concepts have been applied successfully to many investigation tasks, like the localization of the chain recurrent set, attractors, and their domains of attraction as well as the computation of the Morse spectrum and verification of hyperbolicity. However, the field of application is still limited. Reason is that the construction of the symbolic image, which is the basic task of every computation, can require a large amount of memory resources. Hereby, the amount of required resources does not only depend on the dimension of the dynamical system and the performed investigation task but also on the specific characteristics of the system’s dynamics. In this work, we propose methods for the tuning of the construction process. The main idea is to use higher function iterates in order to build the symbolic image. The application of this technique allows a significant reduction of required memory resources so that the investigation methods can be applied in a wider range of scenarios. Differential Equations and Control Processes, N 3, 2005