Motivated by the practical consideration of the measurement of chaotic signals in experiments or the transmission of these signals through a physical medium, we investigate the effect of filtering on chaotic symbolic dynamics. We focus on the linear, time-invariant filters that are used frequently in many applications, and on the two quantities characterizing chaotic symbolic dynamics: topologi...

In Cognitive Science, recently Dynamical Systems Theory (DST) has been advocated as an approach to cognitive modelling that is better suited to the dynamics of cognitive processes than the symbolic/computational approaches are. Often the differences between DST and the symbolic/computational approach are emphasized. However, if two approaches are used also their commonalities can be analysed, a...

There is no universal measure of complexity. When the problem under study leads to description by means of symbolic sequences, formal language theory may provide a convenient framework for analysis. In this review we concentrate on a special class of languages, namely, factorizable languages to be defined later, which occur in many problems of dynamics and biology. In dynamics we have in mind s...

A practical and popular technique to extract the symbolic dynamics from experimentally measured chaotic time series is the threshold-crossing method, by which an arbitrary partition is utilized for determining the symbols. We address to what extent the symbolic dynamics so obtained can faithfully represent the phase-space dynamics. Our principal result is that such a practice can lead to a seve...

dynamics, a hybrid control system is a particular type of hybrid dynamical system. Motivation. Hybrid dynamical systems are ubiquitous in science and engineering as they permit capturing In: Handbook of networked and embedded. Symbolic Dynamics and Dynamical System Models PDF generated using the open Dynamical Systems and Symbolic Dynamics 2 Dynamical system 2 to Time series Analysis (Engineeri...