Search results for "Quasiperiodic function"
showing 10 items of 26 documents
Hidden Strange Nonchaotic Attractors
2021
In this paper, it is found numerically that the previously found hidden chaotic attractors of the Rabinovich–Fabrikant system actually present the characteristics of strange nonchaotic attractors. For a range of the bifurcation parameter, the hidden attractor is manifestly fractal with aperiodic dynamics, and even the finite-time largest Lyapunov exponent, a measure of trajectory separation with nearby initial conditions, is negative. To verify these characteristics numerically, the finite-time Lyapunov exponents, ‘0-1’ test, power spectra density, and recurrence plot are used. Beside the considered hidden strange nonchaotic attractor, a self-excited chaotic attractor and a quasiperiodic at…
KAM Techniques for Time Dependent Quantum Systems
1995
We consider a spin 1/2 in constant magnetic field perturbed by a quasiperiodic time dependent magnetic field. We discuss its stability properties in terms of the spectrum of the corresponding quasienergy operator. Since the spectrum of the unperturbed problem is dense, there appear small denominators in the perturbation theory, corresponding to resonances. They are treated with a technique developped by L.H. Eliasson, based on a KAM iteration.
Polymorphic and regular localized activity structures in a two-dimensional two-component reaction–diffusion lattice with complex threshold excitation
2010
Abstract Space–time dynamics of the system modeling collective behaviour of electrically coupled nonlinear units is investigated. The dynamics of a local cell is described by the FitzHugh–Nagumo system with complex threshold excitation. It is shown that such a system supports formation of two distinct kinds of stable two-dimensional spatially localized moving structures without any external stabilizing actions. These are regular and polymorphic structures. The regular structures preserve their shape and velocity under propagation while the shape and velocity as well as other integral characteristics of polymorphic structures show rather complex temporal behaviour. Both kinds of structures r…
Large-amplitude Quasiperiodic Pulsations as Evidence of Impulsive Heating in Hot Transient Loop Systems Detected in the EUV with SDO/AIA
2019
Short heat pulses can trigger plasma pressure fronts inside closed magnetic tubes in the corona. The alternation of condensations and rarefactions from the pressure modes drive large-amplitude pulsations in the plasma emission. Here we show the detection of such pulsations along magnetic tubes that brighten transiently in the hot 94A EUV channel of SDO/AIA. The pulsations are consistent with those predicted by hydrodynamic loop modeling, and confirm pulsed heating in the loop system. The comparison of observations and model provides constraints on the heat deposition: a good agreement requires loop twisting and pulses deposited close to the footpoints with a duration of 0.5 min in one loop,…
Rich dynamics and anticontrol of extinction in a prey-predator system
2019
This paper reveals some new and rich dynamics of a two-dimensional prey-predator system and to anticontrol the extinction of one of the species. For a particular value of the bifurcation parameter, one of the system variable dynamics is going to extinct, while another remains chaotic. To prevent the extinction, a simple anticontrol algorithm is applied so that the system orbits can escape from the vanishing trap. As the bifurcation parameter increases, the system presents quasiperiodic, stable, chaotic and also hyperchaotic orbits. Some of the chaotic attractors are Kaplan-Yorke type, in the sense that the sum of its Lyapunov exponents is positive. Also, atypically for undriven discrete sys…
m-bonacci metamaterial multilayers: location of the zero-average index bandgap edges
2009
We examine quasiperiodic multilayers arranged in m-bonacci sequences, which combine ordinary positiveindex materials and dispersive metamaterials with negative index in a certain frequency range. When the volume-averaged refractive index of the nonperiodic multilayer equals zero, the structure does not propagate light radiation and exhibits a forbidden band. We identify some analytical expressions to determine the upper and lower limits of the above zero-average refractive-index bandgap. We recognize that these limits are not explicitly dependent on the geometrical parameters of the stack of layers. © 2009 Optical Society of America. Fil: Monsoriu, J.A.. Universidad Politécnica de Valencia;…
Gravitational waves from oscillating accretion tori: Comparison between different approaches
2005
Quasi-periodic oscillations of high density thick accretion disks orbiting a Schwarzschild black hole have been recently addressed as interesting sources of gravitational waves. The aim of this paper is to compare the gravitational waveforms emitted from these sources when computed using (variations of) the standard quadrupole formula and gauge-invariant metric perturbation theory. To this goal we evolve representative disk models using an existing general relativistic hydrodynamics code which has been previously employed in investigations of such astrophysical systems. Two are the main results of this work: First, for stable and marginally stable disks, no excitation of the black hole quas…
Quantum walk with a time-dependent coin
2006
We introduce quantum walks with a time-dependent coin, and show how they include, as a particular case, the generalized quantum walk recently studied by Wojcik et al. {[}Phys. Rev. Lett. \textbf{93}, 180601(2004){]} which exhibits interesting dynamical localization and quasiperiodic dynamics. Our proposal allows for a much easier implementation of this particular rich dynamics than the original one. Moreover, it allows for an additional control on the walk, which can be used to compensate for phases appearing due to external interactions. To illustrate its feasibility, we discuss an example using an optical cavity. We also derive an approximated solution in the continuous limit (long--wavel…
Unitary time-dependent superconvergent technique for pulse-driven quantum dynamics
2003
We present a superconvergent Kolmogorov-Arnold-Moser type of perturbation theory for time-dependent Hamiltonians. It is strictly unitary upon truncation at an arbitrary order and not restricted to periodic or quasiperiodic Hamiltonians. Moreover, for pulse-driven systems we construct explicitly the KAM transformations involved in the iterative procedure. The technique is illustrated on a two-level model perturbed by a pulsed interaction for which we obtain convergence all the way from the sudden regime to the opposite adiabatic regime.
Imprints of superfluidity on magnetoelastic quasiperiodic oscillations of soft gamma-ray repeaters.
2013
Our numerical simulations show that axisymmetric, torsional, magnetoelastic oscillations of magnetars with a superfluid core can explain the whole range of observed quasiperiodic oscillations (QPOs) in the giant flares of soft gamma-ray repeaters. There exist constant phase QPOs at $f\ensuremath{\lesssim}150\text{ }\text{ }\mathrm{Hz}$ and resonantly excited high-frequency QPOs ($fg500\text{ }\text{ }\mathrm{Hz}$), in good agreement with observations. The range of magnetic field strengths required to match the observed QPO frequencies agrees with that from spin-down estimates. These results suggest that there is at least one superfluid species in magnetar cores.