Search results for "Linear system"
showing 10 items of 1558 documents
Noise removal using a nonlinear two-dimensional diffusion network
1998
Un reseau electrique non lineaire bidimensionnel, constitue de N×N cellules identiques, et modelisant l’equation de Nagumo discrete est presente. A l’aide d’une nouvelle description de la fonction non lineaire, on peut predire analytiquement l’evolution temporelle de la partie coherente du signal, ainsi que celle des perturbations de petites amplitudes qui lui sont superposees. Enfin, des applications a l’amelioration du rapport signal sur bruit, ou au traitement d’images sont suggerees.
Global dynamical behaviors in a physical shallow water system
2016
International audience; The theory of bifurcations of dynamical systems is used to investigate the behavior of travelling wave solutions in an entire family of shallow water wave equations. This family is obtained by a perturbative asymptotic expansion for unidirectional shallow water waves. According to the parameters of the system, this family can lead to different sets of known equations such as Camassa-Holm, Korteweg-de Vries, Degasperis and Procesi and several other dispersive equations of the third order. Looking for possible travelling wave solutions, we show that different phase orbits in some regions of parametric planes are similar to those obtained with the model of the pressure …
Experimental and numerical enhancement of Vibrational Resonance in a neural circuit
2012
International audience; A neural circuit exactly ruled by the FitzHugh-Nagumo equations is excited by a biharmonic signal of frequencies f and F with respective amplitudes A and B. The magnitude spectrum of the circuit response is estimated at the low frequency driving f and presents a resonant behaviour versus the amplitude B of the high frequency. For the first time, it is shown experimentally that this Vibrational Resonance effect is much more pronounced when the two frequencies are multiple. This novel enhancement is also confirmed by numerical predictions. Applications of this nonlinear effect to the detection of weak stimuli are finally discussed.
Nonlinear multipliers and applications
1985
International audience
On the analytical expression of the multicompacton and some exact compact solutions of a nonlinear diffusive Burgers’type equation
2018
International audience; We consider the nonlinear diffusive Burgers' equation as a model equation for signals propagation on the nonlinear electrical transmission line with intersite nonlinearities. By applying the extend sine-cosine method and using an appropriate modification of the Double-Exp function method, we successfully derived on one hand the exact analytical solutions of two types of solitary waves with strictly finite extension or compact support: kinks and pulses, and on the other hand the exact solution for two interacting pulse solitary waves with compact support. These analytical results indicate that the speed of the pulse compactons doesn't depends explicitly on the pulse a…
Flaticon pulses in optical fibers
2014
International audience; We experimentally investigate the nonlinear reshaping of a continuous wave which leads to chirp-free and flat-top intense pulses or flaticons exhibiting strong temporal oscillations at their edges and a stable self-similar expansion upon propagation of their central region.
High third and second order non linearities of chalcogenide glasses and fibers for compact infrared non linear devices.
2008
Due to their intrinsic nature, chalcogenide glasses present attractive nonlinearities from third and second order, with values reaching between 10 and 1000 times those of silica. We present a study of their properties and their shaping with the purpose to reach efficient devices in the near-mid infrared.
Quasi-phase-matched third harmonic generation in optical fibers using refractive-index gratings
2011
International audience; The purpose of this work is to demonstrate the quasi-phase-matching of third harmonic generation process in optical fibers using refractive-index gratings. We compare conversion efficiency calculated with analytical coupled modes theory and numerical approach employing system of coupled generalized nonlinear Schrödinger equation. Moreover, we show that introducing the phase matching condition that takes into account the nonlinear contribution to propagation constants significantly increases the conversion efficiency by several orders of magnitude. Finally we optimize the grating constant to maximize conversion efficiency.
Nonlinear spatial self-cleaning in multimode amplifying fiber and fiber laser cavity
2017
During the last years, multimode fibers (MMFs) were used as an experimental platform for the observation of complex nonlinear propagation phenomena, thanks to their additional spatiotemporal degrees of freedom with respect to single mode fibers. Multimode solitons [1], geometric parametric instability [2], self-induced beam cleaning (SBC) [3] and supercontinuum generation have been reported [4]. In all of these situations considered so far the MMFs were standard graded-index fibers: the intermodal interactions took place in a conservative system (propagation losses were negligible). In this work we have experimentally investigated the Kerr SBC in three dissipative systems: a MMF with signif…
Influence of third-order dispersion on the propagation of incoherent light in optical fibers
2010
International audience; We study the influence of third-order dispersion effects on the propagation of an incoherent nonlinear wave in an optical fiber system. The wave spectrum is shown to exhibit a highly asymmetric deformation characterized by a lateral spectral shoulder and the subsequent formation of an unexpected constant spectral pedestal. A kinetic approach to the problem reveals the existence of an invariant that explains in detail the essential properties of such asymmetric spectral evolution of the wave.