Symbolic dynamics plays a central role in the description of the evolution of nonlinear systems. However, there are few reliable methods for determining the symbolic dynamics of chaotic experimental time series. One of the major di culties is that the experimental data contains both the chaotic dynamics of the underlying deterministic system and the random uctuations produced by stochastic pert...

We give a new proof of the Cobham’s first theorem using ideas from symbolic dynamics and of the Cobham-Semenov theorem (in the primitive case) using ideas from tiling dynamics.

The analysis of symbolic dynamics applied to physiological time series retrieves dynamical properties of the underlying regulation which are robust against the symbolic transformation. In this study, three different transformations to produce a symbolic series were applied to fetal RR interval series to test whether they reflect individual changes of fetal heart rate variability in the course o...

We construct a well ordered symbolic dynamics plane for the stadium billiard. In this symbolic plane the forbidden and the allowed orbits are separated by a monotone pruning front, and allowed orbits can be systematically generated by sequences of approximate finite grammars. 1 ‡ Permanent address: Phys Dep., University of Oslo, Box 1048, Blindern, N-0316 Oslo

Ordinal symbolic analysis opens an interesting and powerful perspective on time-series analysis. Here, we review this relatively new approach and highlight its relation to symbolic dynamics and representations. Our exposition reaches from the general ideas up to recent developments, with special emphasis on its applications to biomedical recordings. The latter will be illustrated with epilepsy ...

The present study aims at improving the ability of the canonical genetic programming algorithm to solve problems, and describes an improved genetic programming (IGP). The proposed method can be described as follows: the first investigates initializing population, the second investigates reproduction operator, the third investigates crossover operator, and the fourth investigates mutation operat...

We present results on symbolic reachability analysis for hybrid systems with linear autonomous dynamics in each location.

We show how a simple scheme of symbolic dynamics distinguishes a chaotic from a random time series and how it can be used to detect structural relationships in coupled dynamics. This is relevant for the question at which scale in complex dynamics regularities and patterns emerge. 1 Symbolic dynamics distinguishing chaotic from random dynamics 1.1 Random sequences and dynamical iterates Accordin...

Giovanni Sirio Carmantini Dynamical Systems Theory for Transparent Symbolic Computation in Neuronal Networks In this thesis, we explore the interface between symbolic and dynamical system computation, with particular regard to dynamical system models of neuronal networks. In doing so, we adhere to a definition of computation as the physical realization of a formal system, where we say that a dy...

Recent work has considered the possibility of utilizing symbolic representations of controlled chaotic orbits for communicating with chaotically behaving signal generators. The success of this type of nonlinear digital communication scheme relies on partitioning the phase space properly so that a good symbolic dynamics can be defined. A central problem is then how to encode an arbitrary message...