Related papers: Analysis and separation of time-frequency componen…
The performances of a new data processing technique, namely the Empirical Mode Decomposition, are evaluated on a fully developed turbulent velocity signal perturbed by a numerical forcing which mimics a long-period flapping. First, we…
Nonlinear time series analysis is an active field of research that studies the structure of complex signals in order to derive information of the process that generated those series, for understanding, modeling and forecasting purposes. In…
The study of experimental data is a relevant task in several physical, chemical and biological applications. In particular, the analysis of chaotic dynamics in cardiac systems is crucial as it can be related to some pathological…
The content of this contribution is based on the course on numerical analysis techniques for non-linear dynamics. After introducing basic concepts as the visual analysis of trajectories in phase space and the importance of the nature of…
The Synchrosqueezing transform is a time-frequency analysis method that can decompose complex signals into time-varying oscillatory components. It is a form of time-frequency reassignment that is both sparse and invertible, allowing for the…
Although classical spectral analysis is a natural approach to characterise linear systems, it cannot describe a chaotic dynamics. Here, we propose the ordinal spectrum, a method based on a spectral transformation of symbolic sequences, to…
We demonstrate the utility of machine learning in the separation of superimposed chaotic signals using a technique called Reservoir Computing. We assume no knowledge of the dynamical equations that produce the signals, and require only…
Neural signals are characterized by rich temporal and spatiotemporal dynamics that reflect the organization of cortical networks. Theoretical research has shown how neural networks can operate at different dynamic ranges that correspond to…
The long therm behavior of chaotic flows is investigated by means of time dependent frequency analysis. The system under test consists of an electrically conducting fluid, confined between two differentially rotating spheres. The spherical…
A method is described for the detection and estimation of transient chirp signals that are characterized by smoothly evolving, but otherwise unmodeled, amplitude envelopes and instantaneous frequencies. Such signals are particularly…
Certain deterministic non-linear systems may show chaotic behaviour. Time series derived from such systems seem stochastic when analyzed with linear techniques. However, uncovering the deterministic structure is important because it allows…
The chaotic synchronization of two electron-wave media with interacting backward waves and cubic phase nonlinearity is investigated in the paper. To detect the chaotic synchronization regime we use a new approach, the so-called time scale…
Analytical solutions to the chaotic and ergodic motion of a certain class of one-dimensional dissipative and discrete dynamical systems are derived. This allows us to obtain exact expressions for physical properties like the time…
Chaotic systems that decompose into two cells connected only by a narrow channel exhibit characteristic deviations of their quantum spectral statistics from the canonical random-matrix ensembles. The equilibration between the cells…
In many applications, it is necessary to retrieve the sub-signal building blocks of a multi-component signal, which is usually non-stationary in real-world and real-life applications. Empirical mode decomposition (EMD), synchrosqueezing…
We propose a new unsupervised and non-parametric method to detect change points in intricate quasi-periodic signals. The detection relies on optimal transport theory combined with topological analysis and the bootstrap procedure. The…
Extracting reliable indicators of chaos from a single experimental time series is a challenging task, in particular, for systems with many degrees of freedom. The techniques available for this purpose often require unachievably long time…
In this paper, we consider multiple signals sharing same instantaneous frequencies. This kind of data is very common in scientific and engineering problems. To take advantage of this special structure, we modify our data-driven…
In this paper a new method of detection of homogeneous zones and singularity parts of a 1D signal is proposed. The entropy function is used to transform signal in piecewise linear one. The multiple regression permits to detect lines and…
We formulate a linear phase and frequency response theory for hyperbolic flows, which generalizes phase response theory for autonomous limit cycle oscillators to hyperbolic chaotic dynamics. The theory is based on a shadowing conjecture,…