Related papers: A highly specific test for periodicity

A method for testing nonlinearity in time series is described based on information-theoretic functionals -- redundancies, linear and nonlinear forms of which allow either qualitative, or, after incorporating the surrogate data technique,…

The existence of periodic solutions is proven for some neuroscience models with a small parameter. Moreover, the stability of such solutions is investigated, as well. The results are based on a theoretical research dealing with the…

We propose a new class of univariate nonstationary time series models, using the framework of modulated time series, which is appropriate for the analysis of rapidly-evolving time series as well as time series observations with missing…

We present a systematic methodology to determine and locate analytically isolated periodic points of discrete and continuous dynamical systems with algebraic nature. We apply this method to a wide range of examples, including a…

The variety of complex algorithmic approaches for tackling time-series classification problems has grown considerably over the past decades, including the development of sophisticated but challenging-to-interpret deep-learning-based…

Species subject to predation and environmental threats commonly exhibit variable periods of population boom and bust over long timescales. Understanding and predicting such behavior, especially given the inherent heterogeneity and…

One of the main features of interest in analysing the light curves of stars is the underlying periodic behaviour. The corresponding observations are a complex type of time series with unequally spaced time points and are sometimes…

In this work, we address the problem of identifying sparse continuous-time dynamical systems when the spacing between successive samples (the sampling period) is not constant over time. The proposed approach combines the…

Space missions such as Kepler and CoRoT have led to large numbers of eclipse or transit measurements in nearly continuous time series. This paper shows how to obtain the period error in such measurements from a basic linear least-squares…

A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying…

We propose a method that is able to analyze chaotic time series, gained from exp erimental data. The method allows to identify scalar time-delay systems. If the dynamics of the system under investigation is governed by a scalar time-delay…

Time series data from real-world systems often display non-stationary behavior, indicating varying statistical characteristics over time. This inherent variability poses significant challenges in deciphering the underlying structural…

Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbolic but is normally…

We propose a time-adaptive predictor/multi-corrector method to solve hyperbolic partial differential equations, based on the generalized-$\alpha$ scheme that provides user-control on the numerical dissipation and second-order accuracy in…

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 search for patterns in time series is a very common task when dealing with complex systems. This is usually accomplished by employing a complexity measure such as entropies and fractal dimensions. However, such measures usually only…

Time series analysis has proven to be a powerful method to characterize several phenomena in biology, neuroscience and economics, and to understand some of their underlying dynamical features. Despite a plethora of methods have been…

The synchronization analysis of limit-cycle oscillators is prevalent in many fields, including physics, chemistry, and life sciences. It relies on the phase calculation that utilizes measurements. However, the synchronization of…

An existing dialogue between number theory and dynamical systems is advanced. A combinatorial device gives necessary and sufficient conditions for a sequence of non-negative integers to count the periodic points in a dynamical system. This…

Discovering causal relations from observational time series without making the stationary assumption is a significant challenge. In practice, this challenge is common in many areas, such as retail sales, transportation systems, and medical…