Related papers: Analysis and separation of time-frequency componen…
Purpose: Chaotic diffusion in the non-linear systems is commonly studied in the action framework. In this paper, we show that the study in the frequency domain provides good estimates of the sizes of the chaotic regions in the phase space,…
It is shown that a relevant control of Hamiltonian chaos is possible through suitable small perturbations whose form can be explicitly computed. In particular, it is possible to control (reduce) the chaotic diffusion in the phase space of a…
A new method is introduced for analysis of interactions between time-dependent coupled oscillators, based on the signals they generate. It distinguishes unsynchronized dynamics from noise-induced phase slips, and enables the evolution of…
A new approach is proposed to the quantitative estimation of the complexity of multidimensional discrete sequences in terms of the shapes of their trajectories in the extended space of states. This approach is based on the study of the…
We experimentally demonstrate and numerically simulate a new adaptive method to maintain synchronization between coupled nonlinear chaotic oscillators, when the coupling between the systems is unknown and time-varying (e.g., due to…
Time reversal mirrors have been successfully implemented for various kinds of waves propagating in complex media. In particular, acoustic waves in chaotic cavities exhibit a refocalization that is extremely robust against external…
Classical regular and chaotic dynamics of the particle bound in the Coulomb plus linear potential under the influence of time-periodical perturbations is treated using resonace analysis. Critical value of the external field at which…
We demonstrate by means of a simple example that the arbitrariness of defining a phase from an aperiodic signal is not just an academic problem, but is more serious and fundamental. Decomposition of the signal into components with positive…
In the present work we investigate phase correlations by recourse to the Shannon entropy. Using theoretical arguments we show that the entropy provides an accurate measure of phase correlations in any dynamical system, in particular when…
Classically integrable approximants are here constructed for a family of predominantly chaotic periodic systems by means of the Baker-Hausdorff-Campbell formula. We compare the evolving wave density for the corresponding exact quantum…
The scattering phase shift encodes a good amount of physical information which can be used to study resonances from scattering data. Among others, it can be used to calculate the continuum density of states and the collision time in a…
This paper presents the result of the investigation of chaotic oscillator synchronization. A new approach for detecting of synchronized behaviour of chaotic oscillators has been proposed. This approach is based on the analysis of different…
The applicability of machine learning for predicting chaotic dynamics relies heavily upon the data used in the training stage. Chaotic time series obtained by numerically solving ordinary differential equations embed a complicated noise of…
We investigate how dynamical decoupling methods may be used to manipulate the time evolution of quantum many-body systems. These methods consist of sequences of external control operations designed to induce a desired dynamics. The systems…
The Hopf oscillator has been shown to capture many phenomena of the auditory and vestibular systems. These systems exhibit remarkable temporal resolution and sensitivity to weak signals, as they are able to detect sounds that induce motion…
Context: Several approaches to estimate frequency, phase and amplitude errors in time series analyses were reported in the literature, but they are either time consuming to compute, grossly overestimating the error, or are based on…
This paper describes a method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms. The method allows calculating efficiently the transforms of a signal having an arbitrary dimension of the digital…
Consistency and predictability of brain functionalities depend on reproducible activity of a single neuron. We identify a reproducible non-chaotic neuronal phase where deviations between concave response latency profiles of a single neuron…
Many complex phenomena, from weather systems to heartbeat rhythm patterns, are effectively modeled as low-dimensional dynamical systems. Such systems may behave chaotically under certain conditions, and so the ability to detect chaos based…
Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…