Related papers: Description of stochastic and chaotic series using…
The visibility algorithm has been recently introduced as a mapping between time series and complex networks. This procedure allows to apply methods of complex network theory for characterizing time series. In this work we present the…
Visibility algorithms are a family of methods to map time series into networks, with the aim of describing the structure of time series and their underlying dynamical properties in graph-theoretical terms. Here we explore some properties of…
This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear…
The horizontal visibility algorithm has been recently introduced as a mapping between time series and networks. The challenge lies in characterizing the structure of time series (and the processes that generated those series) using the…
Correlations in multifractal series have been investigated, extensively. Almost all approaches try to find scaling features of a given time series. However, the analysis of such scaling properties has some difficulties such as finding a…
In order to extract correlation information inherited in stochastic time series, the visibility graph algorithm has been recently proposed, by which a time series can be mapped onto a complex network. We demonstrate that the visibility…
In the last decade, there has been a growing body of literature addressing the utilization of complex network methods for the characterization of dynamical systems based on time series. While both nonlinear time series analysis and complex…
Visibility algorithms transform time series into graphs and encode dynamical information in their topology, paving the way for graph-theoretical time series analysis as well as building a bridge between nonlinear dynamics and network…
The non-stationary evolution of observable quantities in complex systems can frequently be described as a juxtaposition of quasi-stationary spells. Given that standard theoretical and data analysis approaches usually rely on the assumption…
The limited penetrable horizontal visibility algorithm is a new time analysis tool and is a further development of the horizontal visibility algorithm. We present some exact results on the topological properties of the limited penetrable…
Visibility algorithms are a family of geometric and ordering criteria by which a real-valued time series of N data is mapped into a graph of N nodes. This graph has been shown to often inherit in its topology non-trivial properties of the…
The family of visibility algorithms were recently introduced as mappings between time series and graphs. Here we extend this method to characterize spatially extended data structures by mapping scalar fields of arbitrary dimension into…
In this work we present a simple and fast computational method, the visibility algorithm, that converts a time series into a graph. The constructed graph inherits several properties of the series in its structure. Thereby, periodic series…
Nonlinear time series analysis is becoming a more and more reliable tool for the study of complicated dynamics from measurements. The concept of low-dimensional chaos has proven to be fruitful in the understanding of many complex phenomena…
We use standard deep neural networks to classify univariate time series generated by discrete and continuous dynamical systems based on their chaotic or non-chaotic behaviour. Our approach to circumvent the lack of precise models for some…
In 1980 and 1981, two pioneering papers laid the foundation for what became known as nonlinear time-series analysis: the analysis of observed data---typically univariate---via dynamical systems theory. Based on the concept of state-space…
Many applications collect a large number of time series, for example, the financial data of companies quoted in a stock exchange, the health care data of all patients that visit the emergency room of a hospital, or the temperature sequences…
Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be…
Recently, the visibility graph has been introduced as a novel view for analyzing time series, which maps it to a complex network. In this paper, we introduce new algorithm of visibility, "cross-visibility", which reveals the conjugation of…
A method is proposed to generate an optimal fit of a number of connected linear trend segments onto time-series data. To be able to efficiently handle many lines, the method employs a stochastic search procedure to determine optimal…