Search results for "Pattern formation"
showing 10 items of 408 documents
Effet d’une perturbation haute fréquence sur la réponse du système de FitzHugh-Nagumo soumis à une excitation basse fréquence subliminale : simulatio…
2015
National audience; Dans cette communication, nous menons conjointement une étude en simulation numérique ainsi qu’une étude expérimentale de la réponse du système de FitzHugh-Nagumo soumis à une excitation bi-chromatique. Cette excitation est constituée d’un signal basse fréquence perturbé par une composante haute fréquence additive. Selon l’amplitude B de la perturbation haute fréquence, la réponse du système peut être optimisée à la basse fréquence. Un choix approprié du rapport des fréquences d’excitations peut conduire à une meilleure optimisation de la réponse du système.
Génération expérimentale de solitons de cut-off dans une ligne électrique non linéaire
2015
National audience; Nous étudions le phénomène de supratransmission dans un milieu non linéaire discret, soumis, à une excitation périodique dont la fréquence appartient à la bande interdite. Nous montrons l’existence d’un seuil de tension au dessus duquel l’instabilité modulationnelle (IM) va se développer dans la ligne, valeur de seuil dépendant de la fréquence d’excitation. Si elle n’empêche pas l’apparition de l’IM par supratransmission, la dissipation présente dans la ligne est un obstacle à la génération des solitons de cut-off, obstacle que nous sommes parvenus à contourner par un choix approprié de l’amplitude de l’excitation.
Bifurcations of Phase Portraits of a Singular Nonlinear Equation of the Second Class
2014
International audience; The soliton dynamics is studied using the Frenkel Kontorova (FK) model with non- convex interparticle interactions immersed in a parameter ized on-site substrate po- tential. The case of a deformable substrate potential allow s theoretical adaptation of the model to various physical situations. Non-convex inter actions in lattice systems lead to a number of interesting phenomena that cannot be prod uced with linear coupling alone. In the continuum limit for such a model, the p articles are governed by a Singular Nonlinear Equation of the Second Class. The dyn amical behavior of traveling wave solutions is studied by using the theory of bi furcations of dynamical syst…
Statistical mechanics of nonclassic solitonic structures-bearing dna system
2011
International audience
Supratransmission dans une ligne électrique de Klein-Gordon
2017
National audience; Nous présentons une ligne électrique dont la tension obéit aux équations de Klein-Gordon d’ordre 5afin d’en étudier les propriétés de transmission. Nous focalisons sur la transmission d’énergie en bande interdite,c’est à dire lorsque le système est excité en dehors de sa bande passante. Nous avons pu expérimentallement mettreen évidence que lorsque l’amplitude de l’excitation excède un seuil, le système génére des modes non linéaires deforte amplitude via le phénomène de supratransmission.
Energy transmission in the gap of nonlinear media triggered by deterministic and stochastic driving
2016
International audience; These past years, a growing interest has been devoted to the analysis of the response of nonlinearmedia to various excitations wether random or deterministic in order to better characterizetheir transmission properties [1, 2, 3]. Especially, since the introduction of the concept of soliton,the development of nonlinear electrical transmission lines has provided an efficient tool toexperimentally investigate the behaviour of these nonlinear waves [4]. Recently, some effortshave focused on the energy transmission in the gap of media obeying to equations deriving fromthe nonlinear Schr¨odinger model [5, 6]. Indeed, Geniet and Leon have shown that such nonlinearsystems, w…
From finite-gap solutions of KdV in terms of theta functions to solitons and positons
2010
We degenerate the finite gap solutions of the KdV equation from the general formulation in terms of abelian functions when the gaps tends to points, to recover solutions of KdV equations in terms of wronskians called solitons or positons. For this we establish a link between Fredholm determinants and Wronskians.
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…
Nonlinear topological symmetry protection in a dissipative system
2023
We report an experimental and theoretical investigation of a system whose dynamics is dominated by an intricate interplay between three key concepts of modern physics: topology, nonlinearity, and spontaneous symmetry breaking. The experiment is based on a two-mode coherently-driven optical resonator in which photons interact through the Kerr nonlinearity. In presence of a phase defect between the modes, a nonlinear attractor develops, which confers a synthetic M\"obius topology to the modal structure of the system. That topology is associated with an inherently protected exchange symmetry between the modes, enabling the realization of spontaneous symmetry breaking in ideal, bias-free, condi…
Rains of Solitons in a Fiber Laser
2009
We report a novel and intriguing nonlinear dynamics observed in a fiber laser cavity, in which soliton pulses are created from an extended noisy background and drift until they reach a condensed phase comprising several tens of aggregated solitons. This soliton flow can be adjusted with manual cavity tuning, and can even be triggered by the injection of an external low-power cw laser.