Related papers: Identifying complex periodic windows in continuous…
We study the parametric online changepoint detection problem, where the underlying distribution of the streaming data changes from a known distribution to an alternative that is of a known parametric form but with unknown parameters. We…
Temporal networks are commonly used to represent dynamical complex systems like social networks, simultaneous firing of neurons, human mobility or public transportation. Their dynamics may evolve on multiple time scales characterising for…
We propose a novel approach for analysing time series using complex network theory. We identify the recurrence matrix calculated from time series with the adjacency matrix of a complex network, and apply measures for the characterisation of…
In this paper, we investigate the parameter identification problem in dynamical systems through a deep learning approach. Focusing mainly on second-order, linear time-invariant dynamical systems, the topic of damping factor identification…
We present here two promising techniques for the application of the complex network approach to continuous spatio-temporal systems that have been developed in the last decade and show large potential for future application and development…
We describe a novel method for modeling non-stationary multivariate time series, with time-varying conditional dependencies represented through dynamic networks. Our proposed approach combines traditional multi-scale modeling and network…
An alternative numerical method is developed to find stable and unstable periodic orbits of nonlinear dynamical systems. The method exploits the high-efficiency of the Levenberg-Marquardt algorithm for medium-sized problems and has the…
Magnetic storms constitute the most remarkable large-scale phenomena of nonlinear magnetospheric dynamics. Studying the dynamical organization of macroscopic variability in terms of geomagnetic activity index data by means of complexity…
We present a combinatorial approach to rigorously show the existence of fixed points, periodic orbits, and symbolic dynamics in discrete-time dynamical systems, as well as to find numerical approximations of such objects. Our approach…
We present a novel numerical method aimed to characterize global behaviour, in particular chaotic diffusion, in dynamical systems. It is based on an analysis of the Poincar\'e recurrence statistics on massive grids of initial data or values…
Large-scale coherent structures are identified in turbulent pipe flow at $Re_\tau=181$ by having long lifetimes, living on large scales and travelling with a certain group velocity. A Characteristic Dynamic Mode Decomposition (CDMD) is used…
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…
We integrate machine learning approaches with nonlinear time series analysis, specifically utilizing recurrence measures to classify various dynamical states emerging from time series. We implement three machine learning algorithms Logistic…
Limit cycle oscillations are phenomena arising in nonlinear dynamical systems and characterized by periodic, locally-stable, and self-sustained state trajectories. Systems controlled in a closed loop along a periodic trajectory can also be…
We present Link Density (LD) computed from the Recurrence Network (RN) of a time series data as an effective measure that can detect dynamical transitions in a system. We illustrate its use using time series from the standard Rossler system…
We introduce new machine-learning techniques for analyzing chaotic dynamical systems. The primary objectives of the study include the development of a new and simple method for calculating the Lyapunov exponent using only two trajectory…
This note presents an online pseudospectral method for system identification using Chebyshev polynomial basis under aperiodic sampling. The system dynamics are approximated piecewise by introducing a sliding time window. The number of…
Real world evolves in continuous time but computations are done from finite samples. Therefore, we study algorithms using finite observations in continuous-time linear dynamical systems. We first study the system identification problem, and…
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…
We present a method that allows to distinguish between nearly periodic and strictly periodic time series. To this purpose, we employ a conservative criterion for periodicity, namely that the time series can be interpolated by a periodic…