Related papers: False periods in complex chaotic systems
The unprecedented light curves of the Kepler space telescope document how the brightness of some stars pulsates at primary and secondary frequencies whose ratios are near the golden mean, the most irrational number. A nonlinear dynamical…
Light curves of astrophysical objects frequently contain strictly periodic signals. In those cases we can use that property to aid the detrending algorithm to fully disentangle an unknown periodic signal and an unknown baseline signal with…
A signal processing method designed for the detection of linear (coherent) behaviors among random fluctuations is presented. It is dedicated to the study of data recorded from nonlinear physical systems. More precisely the method is suited…
Searching for combinations in the frequency spectra of variable stars is a commonly used method within the asteroseismological community, as harmonics and linear combinations of individual frequencies are expected to appear not only by…
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 propose a new method for determining the stochastic or ordered nature of trajectories in non-integrable Hamiltonian dynamical systems. The method consists of constructing a time-series from the divergence of nearby trajectories and then…
The discovery of quasi-periodic oscillations (QPOs) in magnetar giant flares has opened up prospects for neutron star asteroseismology. However, with only three giant flares ever recorded, and only two with data of sufficient quality to…
Aperiodic variability is a characteristic feature of young stars, massive stars, and active galactic nuclei. With the recent proliferation of time domain surveys, it is increasingly essential to develop methods to quantify and analyze…
Variability in the light curves of spotted, rotating stars is often non-sinusoidal and quasi-periodic --- spots move on the stellar surface and have finite lifetimes, causing stellar flux variations to slowly shift in phase. A strictly…
Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic…
Many exo-solar systems discovered in the last decade consist of planets orbiting in resonant configurations and consequently, their evolution should show long-term stability. However, due to the mutual planetary interactions a multi-planet…
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…
La plupart des etoiles variables qui pulsent avec grande amplitude, telles les cepheides, ont un comportement tres regulier et periodique. Mais juste a cote d'elles dans le diagramme Hertzsprung-Russell, se trouve un groupe d'etoiles…
We introduce a new analytical method, which allows to find out chaotic dynamics in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered as an example. The corresponding…
We study the nature of motion in a 3D potential composed of perturbed elliptic oscillators. Our technique is to use the results obtained from the 2D potential in order to find the initial conditions generating regular or chaotic orbits in…
We consider the classical response in a chaotic system. In contrast to behavior in integrable or almost integrable systems, the nonlinear classical response in a chaotic system vanishes at long times. The response also reveals certain…
Unstable periodic orbits scar wave functions in chaotic systems. This also influences the associated spectra, that follow the otherwise universal Porter--Thomas intensity distribution. We show here how this deviation extend to other longer…
We investigate the regular or chaotic nature of orbits of stars moving in the meridional plane $(R,z)$ of an axially symmetric galactic model with a flat disk and a central, non spherical and massive nucleus. In particular, we study the…
We introduce a novel technique to find the asymptotic time behaviour of deterministic systems exhibiting anomalous diffusion. The procedure is tested for various classes of simple but physically relevant 1-D maps and possible relevance of…
Droplets moving in a microfluidic loop device exhibit both periodic and chaotic behaviors based on the inlet droplet spacing. We propose that the periodic behavior is an outcome of a dispersed phase conservation principle. This conservation…