Search results for "Attractor"
showing 10 items of 162 documents
Relaxation, postponement, and features of the attractor in a driven varactor oscillator
1990
The driven varactor oscillator is investigated by numerical integration of its ODEs using the standard model of circuit theory. Attention is given to some properties of the basic relaxation mechanism. For time dependent amplitudes of the sinusoidal driving voltage the post-ponement of the bifurcations is characterized by transient Lyapunov numbers. The postponement of the first bifurcation shows the same dependence on the sweep velocity as in the case of the nonautonomous quadratic map. The shapes of the attractors are displayed in extended phase space. Generalized Renyi-dimensionsD 0 andD 1 have been determined in the chaotic region. A corresponding twodimensional Pioncare map indicates se…
Physical interpretation of laser phase dynamics
1990
The basic features characterizing the dynamical evolution of the phase of a detuned-laser field under an unstable regime are physically interpreted in terms of dispersive and dynamical effects. A general method for obtaining any attractor projection containing the phase information is established, which provides evidence for the heteroclinic character of the attractor in the presence of cavity detuning for any emission regime.
Attracteur de polarisation dans les fibres optiques
2004
Nous etudions la dynamique non lineaire des etats de polarisation de deux ondes coherentes ou incoherentes se propageant dans une fibre optique. Nous presentons en particulier un effet original d'attraction de la polarisation.
Phenomenological approaches of inflation and their equivalence
2014
In this work, we analyze two possible alternative and model-independent approaches to describe the inflationary period. The first one assumes a general equation of state during inflation due to Mukhanov, while the second one is based on the slow-roll hierarchy suggested by Hoffman and Turner. We find that, remarkably, the two approaches are equivalent from the observational viewpoint, as they single out the same areas in the parameter space, and agree with the inflationary attractors where successful inflation occurs. Rephrased in terms of the familiar picture of a slowly rolling, canonically normalized scalar field, the resulting inflaton excursions in these two approaches are almost ident…
Experimental observation of modal attraction in optical fibers
2002
We investigate experimentally nonlinear optical attractors based on four-photon mixing interaction of counterpropagating waves in optical fibers.
Structural similarities and differences among attractors and their intensity maps in the laser-Lorenz model
1995
Abstract Numerical studies of the laser-Lorenz model using parameters reasonably accessible for recent experiments with a single mode homogeneously broadened laser demonstrate that the form of the return map of successive peak values of the intensity changes from a sharply cusped map in resonance to a map with a smoothly rounded maximum as the laser is detuned into the period doubling regime. This transformation appears to be related to the disappearance (with detuning) of the heteroclinic structural basis for the stable manifold which exists in resonance. This is in contrast to the evidence reported by Tang and Weiss (Phys. Rev. A 49 (1994) 1296) of a cusped map for both the period doublin…
Models, predictions, and experimental measurements of far-infrared NH3-laser dynamics and comparisons with the Lorenz-Haken model
1995
Dynamics of the intensity and optical field amplitude of a coherently pumped far-infrared NH3-laser are measured and characterized. The experimental findings in certain parameter ranges closely follow the dynamics of the Lorenz model and its generalization for laser systems. Similarities and some specific differences are found in geometrical or statistical characterizations of the attractors. The experimental results are also consistent with the results of a model of optically pumped three-level lasers which takes into account the presence of a multiplicity of velocity groups as well as three-level coherence effects. For a certain region in parameter space, this far more complex model with …
On the Multifractal Character of the Lorenz Attractor
1992
A detailed analysis of the Lorenz attractor in connection with generalized dimensions is presented in this work. Different methods have been employed to estimate these dimensions. Two of them are of standard type. A new method, based on the minimal spanning tree of the point distribution, is extensively tested in this work. It turns out that the Lorenz attractor is very appropriate for being analyzed through this technique, which produces a very clean estimate of the extrema scaling indices α min and α max . The different methods give qualitatively the same result: The Lorenz attractor has a multifractal character
Looking for the imprints of nonlinear structures on the cosmic microwave background
1997
Abstract Many authors have estimated the anisotropies produced by one isolated cosmological non-linear inhomogeneity. This paper is an updated review about these estimates. The main methods used in order to deal with this problem are described. The limitations of these methods are analyzed. Results appear to be particularly interesting in the open non-linear case, in which a general treatment of the anisotropies produced by inhomogeneity distributions is very troublesome. The effects produced by very big structures such as the Great Attractor and the Bootes Void are studied in detail. Some generalities about the origin, detection and features of the Cosmic Microwave Background anisotropies …
Longterm damped dynamics of the extensible suspension bridge
2010
This work is focused on the doubly nonlinear equation, whose solutions represent the bending motion of an extensible, elastic bridge suspended by continuously distributed cables which are flexible and elastic with stiffness k^2. When the ends are pinned, long-term dynamics is scrutinized for arbitrary values of axial load p and stiffness k^2. For a general external source f, we prove the existence of bounded absorbing sets.When f is timeindependent, the related semigroup of solutions is shown to possess the global attractor of optimal regularity and its characterization is given in terms of the steady states of the problem.