Ordinal symbolic dynamics has developed into a valuable method to describe complex systems. Recently, using the concept of transcripts, the coupling behaviour of systems was assessed, combining the properties of the symmetric group with information theoretic ideas. In this contribution, methods from the field of ordinal symbolic dynamics are applied to the characterisation of audio data. Coupli...

In this paper, we introduce a new semantics for hybrid systems called symbolic dynamics. The semantics is constructed in the tradition of denotational semantics of programming languages, which defines the meaning of a construct by a function. The novelty of this approach is that these semantic functions are defined on complex state spaces carrying algebraic and analytic structures. As in the de...

In this report, a control method for the stabilization of periodic orbits for a class of discrete-time systems that are topologically conjugate to symbolic dynamics is proposed and applied to a population model in an ecosystem and the Smale horseshoe map. A periodic orbit is assigned as a target by giving a sequence in which symbols have periodicity. As a consequence, it is shown that any perio...

Metastable attractors and heteroclinic orbits are present in the dynamics of various complex systems. Although their occurrence is well-known, their identification and modeling is a challenging task. The present work reviews briefly the literature and proposes a novel combination of their identification in experimental data and their modeling by dynamical systems. This combination applies recur...

We prove that any Parseval wavelet frame is the projection of an orthonormal wavelet basis for a representation of the Baumslag-Solitar group BS(1, 2) = 〈u, t | utu = t〉. We give a precise description of this representation in some special cases, and show that for wavelet sets, it is related to symbolic dynamics (Theorem 3.14). We show that the structure of the representation depends on the ana...

This paper discusses how a behavior-based robot can construct a "symbolic process" that accounts for its deliberative thinking processes using models of the environment. The paper focuses on two essential problems; one is the symbol grounding problem and the other is how the internal symbolic processes can be situated with respect to the behavioral contexts. We investigate these problems by app...

We describe a method for introducing variations into predeened dance sequences using a chaotic mapping. A symbol sequence representing a dance piece is mapped onto a chaotic trajectory, establishing a symbolic dynamics that links the dance sequence and the attractor structure. A choreographic variation on the original piece is created by generating a trajectory with slightly diierent initial co...

We study a certain class of classical one-dimensional piecewise linear maps. For these systems we introduce an infinite family of Markov partitions in equal cells. The symbolic dynamics generated by these systems is described by bi-stochastic (doubly stochastic) matrices. We analyse the structure of graphs generated from the corresponding symbolic dynamics. We demonstrate that the spectra of qu...

This survey paper is aimed to describe a relatively new branch of symbolic dynamics which we call Arithmetic Dynamics. It deals with explicit arithmetic expansions of reals and vectors that have a “dynamical” sense. This means precisely that they (semi-) conjugate a given continuous (or measure-preserving) dynamical system and a symbolic one. The classes of dynamical systems and their codings c...

This paper presents a new hierarchical mode segmentation of the observed driving behavioral data based on the multi-level abstraction of the underlying dynamics. By synthesizing the ideas of a feature vector definition revealing the dynamical characteristics and an unsupervised clustering technique, the hierarchical mode segmentation is achieved. The identified mode can be regarded as a kind of...