Related papers: Quantifying the irregularity of a time series

We present a methodology to characterize synchronization in time series based on symbolic representations. A symbol is linked to a sequence of numbers through the rank-order of its values. A representation of a time series results after…

Structure of real networked systems, such as social relationship, can be modeled as temporal networks in which each edge appears only at the prescribed time. Understanding the structure of temporal networks requires quantifying the…

We introduce a simple method to estimate the system parameters in continuous dynamical systems from the time series. In this method, we construct a modified system by introducing some constants (controlling constants) into the given…

We characterise the evolution of a dynamical system by combining two well-known complex systems' tools, namely, symbolic ordinal analysis and networks. From the ordinal representation of a time-series we construct a network in which every…

The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…

Limit cycles are self-sustained, closed trajectories in phase space representing (un)-stable, periodic behavior in nonlinear dynamical systems. They underpin diverse natural phenomena, from neuronal firing patterns to engineering…

Recurrence is a fundamental property of dynamical systems, which can be exploited to characterise the system's behaviour in phase space. A powerful tool for their visualisation and analysis called recurrence plot was introduced in the late…

In this paper we introduce the concept of random time changes in dynamical systems. The subordination principle may be applied to study the long time behavior of the random time systems. We show, under certain assumptions on the class of…

In the past few decades considerable effort has been expended in characterizing and modeling financial time series. A number of stylized facts have been identified, and volatility clustering or the tendency toward persistence has emerged as…

In complex systems, external parameters often determine the phase in which the system operates, i.e., its macroscopic behavior. For nearly a century, statistical physics has extensively studied systems' transitions across phases,…

Dynamics of complex systems is studied by first considering a chaotic time series generated by Lorenz equations and adding noise to it. The trend (smooth behavior) is separated from fluctuations at different scales using wavelet analysis…

A rich variety of non-equilibrium dynamical phenomena and processes unambiguously calls for the development of general numerical techniques to probe and estimate a complex interplay between spatial and temporal degrees of freedom in…

Most of the time series in nature are a mixture of signals with deterministic and random dynamics. Thus the distinction between these two characteristics becomes important. Distinguishing between chaotic and aleatory signals is difficult…

This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…

Modelling multivariate circular time series is considered. The cross-sectional and serial dependence is described by circulas, which are analogs of copulas for circular distributions. In order to obtain a simple expression of the dependence…

We discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a…

We present two possible criteria quantifying the degree of classicality of an arbitrary (finite dimensional) dynamical system. The inputs for these criteria are the classical dynamical structure of the system together with the quantum and…

In this work, several random Boolean networks (RBN) are generated and analyzed from two characteristics: their time evolution diagram and their transition diagram. For this purpose, its randomness is estimated using three measures, of which…

Probabilistic forecasting of multivariate time series is essential for various downstream tasks. Most existing approaches rely on the sequences being uniformly spaced and aligned across all variables. However, real-world multivariate time…

In this work, we introduce metrics to evaluate the use of simplified time series in the context of interpretability of a TSC -- a Time Series Classifier. Such simplifications are important because time series data, in contrast to text and…