相关论文: Frequency map analysis and quasiperiodic decomposi…
This work provides a systematic recipe for computing accurate high order Fourier expansions of quasiperiodic invariant circles in area preserving maps. The recipe requires only a finite data set sampled from the quasiperiodic circle. Our…
Phase-amplitude coupling (PAC), a form of cross-frequency interaction, has been implicated in various cognitive functions and, by extension, in neural communication and information integration. Accurately detecting and characterising PAC is…
Dynamical systems, whether continuous or discrete, are used by physicists in order to study non-linear phenomena. In the case of discrete dynamical systems, one of the most used is the quadratic map depending on a parameter. However, some…
Harmonic inversion has already been proven to be a powerful tool for the analysis of quantum spectra and the periodic orbit orbit quantization of chaotic systems. The harmonic inversion technique circumvents the convergence problems of the…
The recently developed generalized Fourier-Galerkin method is complemented by a numerical continuation with respect to the kinetic energy, which extends the framework to the investigation of modal interactions resulting in folds of the…
Several data-driven approaches based on information theory have been proposed for analyzing high-order interactions involving three or more components of a network system. Most of these methods are defined only in the time domain and rely…
The need to Fourier transform data sets with irregular sampling is shared by various domains of science. This is the case for example in astronomy or sismology. Iterative methods have been developed that allow to reach approximate…
We develop a formalism for mapping the exact dynamics of an ensemble of disordered quantum systems onto the dynamics of a single particle propagating along a semi-infinite lattice, with parameters determined by the probability distribution…
Optimal frequency identification in astronomical datasets is crucial for variable star studies, exoplanet detection, and asteroseismology. Traditional period-finding methods often rely on specific parametric assumptions, employ binning…
Among various soft computing approaches for time series forecasting, Fuzzy Cognitive Maps (FCM) have shown remarkable results as a tool to model and analyze the dynamics of complex systems. FCM have similarities to recurrent neural networks…
The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there…
The Heisenberg time-energy relation prevents determination of an atomic transition to better than the inverse of the measurement time. The relation generally applies to frequency estimation of a near-resonant field [1-3], since information…
We present a methodology for detecting non-linearities in data sets based on the characterization of the structural features of the Fourier phase maps. A Fourier phase map is a 2D set of points $M= \{(\phi_{\vec{k}}, \phi_{\vec{k} +…
Fast-sampled models are essential for control design, e.g., to address intersample behavior. The aim of this paper is to develop a non-parametric identification technique for fast-sampled models of systems that have relevant dynamics and…
We investigate numerically and experimentally dynamical systems having three interacting frequencies: a discrete mapping (a circle map), an exactly solvable model (a system of coupled ordinary differential equations), and an experimental…
Two novel methods, one that is experimental and the other comprising a pair of theoretical types (one component that is mathematically rigorous and the other that is of frequency domain computational type), are being used in concert to…
Quantitative helio- and asteroseismology require very precise measurements of the frequencies, amplitudes, and lifetimes of the global modes of stellar oscillation. It is common knowledge that the precision of these measurements depends on…
The dynamics of power grids are governed by a large number of nonlinear differential and algebraic equations (DAEs). To safely operate the system, operators need to check that the states described by these DAEs stay within prescribed limits…
This article introduces an effective generalization of the polar flavor of the Fourier Theorem based on a new method of analysis. Under the premises of the new theory an ample class of functions become viable as bases, with the further…
We extend linear input/output (resolvent) analysis to take into account nonlinear triadic interactions by considering a finite number of harmonics in the frequency domain using the harmonic balance method. Forcing mechanisms that maximize…