0000000000046033
AUTHOR
Patrick Marquié
showing 36 related works from this author
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.
Effet du couplage non linéaire dans un système de sine-Gordon modifié
2016
National audience; Cette Communication porte sur une étude numérique visant à montrer les conditions d'existence du phénomène de supratransmission dans un milieu gouverné par l'équation de sine-gordon à couplage mixte: le couplage linéaire pur étant associé à un couplage non linéaire. Nous montrons également l'effet de la variation du coefficient du couplage non linéaire sur l'amplitude de seuil du signal excitateur nécessaire pour déclencher le phénomène de supratransmission dans le milieu, en maintenant constant le coefficient du couplage linéaire pur.
A nonlinear electronic circuit mimicking the neuronal activity in presence of noise
2013
We propose a nonlinear electronic circuit simulating the neuronal activity in a noisy environment. This electronic circuit is ruled by the set of Bonhaeffer-Van der Pol equations and is excited with a white gaussian noise, that is without external deterministic stimuli. Under these conditions, our circuits reveals the Coherence Resonance signature, that is an optimum of regularity in the system response for a given noise intensity.
Propagation failure in discrete bistable reaction-diffusion systems: Theory and experiments
2001
International audience; Wave front propagation failure is investigated in discrete bistable reaction-diffusion systems. We present a theoretical approach including dissipative effects and leading to an analytical expression of the critical coupling beyond which front propagation can occur as a function of the nonlinearity threshold parameter. Our theoretical predictions are confirmed by numerical simulations and experimental results on an equivalent electrical diffusive lattice.
Analog simulation of neural information propagation using an electrical FitzHugh-Nagumo lattice
2004
International audience; A nonlinear electrical lattice modelling neural information propagation is presented. It is shown that our system is an analog simulator of the FitzHugh-Nagumo equations, and hence supports pulse propagation with the appropriate properties.
Real-time weighting optimization in Chinese Postman Problem
2013
International audience; In this study, based on real-time constraint, an optimization method is proposed for solving the problem of the optimal tour. For that, we will construct a graph containing the real-time state of traffic. The collected data will be used to predict the future state traffic and to give an optimized cost of the tour. This optimization is tested in different sizes of the road networks. The results show that the proposed method is efficient and effective in solving the Chinese Postman Problem in real-time.
Effet du bruit dans le système de sine-Gordon
2015
National audience; Cette communication porte sur une étude numérique visant à montrer que le bruit peut permettre le déclenchement de modes Breather dans le système de sine-Gordon. Dans un premier temps, en l’absence de bruit, le phénomène de supratransmission introduit et quantifié par Geniet et Léon est vérifié : il existe une amplitude critique de l’excitation sinusoıdale au delà de laquelle le milieu transmet de l’énergie bien qu’excité en dehors de sa bande passante. Nous montrons que sous certaines conditions, le bruit peut faciliter l’apparition de ce phénomène de supratransmission et déclencher des modes Breather.
Coherence resonance in Bonhoeffer-Van der Pol circuit
2009
International audience; A nonlinear electronic circuit simulating the neuronal activity in a noisy environment is proposed. This electronic circuit is exactly ruled by the set of Bonhoeffer-Van Der Pol equations and is excited with a Gaussian noise. Without external deterministic stimuli, it is shown that the circuit exhibits the so-called 'coherence resonance' phenomenon.
Ghost stochastic resonance in FitzHugh–Nagumo circuit
2014
International audience; The response of a neural circuit submitted to a bi-chromatic stimulus and corrupted by noise is investigated. In the presence of noise, when the spike firing of the circuit is analysed, a frequency not present at the circuit input appears. For a given range of noise intensities, it is shown that this ghost frequency is almost exclusively present in the interspike interval distribution. This phenomenon is for the first time shown experimentally in a FitzHugh-Nagumo circuit.
Diffusion effects in a nonlinear electrical lattice
1998
International audience; We consider a nonlinear electrical network modeling the generalized Nagumo equation. Focusing on the particular case where the initial load of the lattice consists in the superimposition of a coherent information weakly varying in space and a perturbation of small amplitude, we show that the perturbation can be eliminated quickly, almost without disturbing the information.
Experimental observation of the generation of cutoff solitons in a discreteLCnonlinear electrical line
2014
We address the problem of supratransmission of waves in a discrete nonlinear system, driven at one end by a periodic excitation at a frequency lying above the phonon band edge. In an experimental electrical transmission line made of 200 inductance-capacitance LC cells, we establish the existence of a voltage threshold for a supratransmission enabling the generation and propagation of cut-off solitons within the line. The decisive role of modulational instability in the onset and development of the process of generation of cut-off solitons is clearly highlighted. The phenomenon of dissipation is identified as being particularly harmful for the soliton generation, but we show that its impact …
Nonlinear Schrödinger models and modulational instability in real electrical lattices
1995
International audience; In nonlinear dispersive media, the propagation of modulated waves, such as envelope (bright) solitons or hole (dark) solitons, has been the subject of considerable interest for many years, as for example in nonlinear optics [A.C. Newell and J.V. Moloney, Nonlinear Optics (Addison-Presley, 1991)]. On the other hand, discrete electrical transmission lines are very convenient tools to study the wave propagation in 1D nonlinear dispersive media [A.C. Scott (Wiley-Interscience, 1970)]. In the present paper, we study the generation of nonlinear modulated waves in real electrical lattices. In the continuum limit, our theoretical analysis based on the Nonlinear Schrodinger e…
Dispersion-managed electrical transmission lines
2009
International audience; We examine the ability of electrical pulses to execute a highly stable propagation in a special electrical network made of concatenated pieces of discrete electrical lines with alternately positive and negative signs of the second-order dispersion. We show that such networks, called dispersion-managed electrical lines, induce a pulse breathing phenomenon, that is a dynamical behaviour with alternate regimes of pulse broadening and compression. This breathing phenomenon, which prevents the pulse from broadening without bounds during propagation in the network is the most appealing feature of the technique of dispersion management developed in the last decade in the ar…
Chaotic-like behavior of modulated waves in a nonlinear discrete LC transmission line
2003
International audience; Modulational instability (MI) in a discrete nonlinear LC transmission line is investigated. The higher order nonlinear Schrodinger (NLS) equation modeling modulated waves propagation in the network allows to predict the MI conditions, with additional features, compared to the standard NLS model. More precisely, a chaotic-like behavior of the system, which is observed in a particular frequency domain, is related to the nonrepeatability of the numerical experiments.
On Some Applications of Nonlinear Differential Equations in Image Processing: Concepts and Electronic Implementation
2011
International audience
Energy localization in a nonlinear discrete system
1996
International audience; We show that, in the weak amplitude and slow time limits, the discrete equations describing the dynamics of a one-dimensional lattice can be reduced to a modified Ablowitz-Ladik equation. The stability of a continuous wave solution is then investigated without and with periodic boundary conditions; Energy localization via modulational instability is predicted. Our numerical simulations, performed on a cyclic system of six oscillators, agree with our theoretical predictions.
Pattern dynamics in a nonlinear electrical lattice
2003
International audience; In this paper, we present experiments using a nonlinear electrical line, modeling the FitzHugh-Nagumo equation, without recovery term. Different patterns are studied according to the para meters of this medium and initial conditions. We then propose to apply these results to the domain of signal processing. We show that erosion and dilation of a binary signal, two kinds,of binarization-one depending on an amplitude threshold, the other on an energetical threshold-and nonlinear filtering allowing noise removal can be obtained in the same medium.
Long-time dynamics of modulated waves in a nonlinear discrete LC transmission line.
2003
International audience; The long-time dynamics of modulated waves in a nonlinear LC transmission line is investigated. Considering the higher-order nonlinear Schrodinger equation, we define analytically the conditions leading to the instability of modulated waves. We show that two kinds of instabilities may develop in the network depending on the frequency range of the chosen carrier wave and on the magnitude of its initial amplitude, which is confirmed by our numerical simulations. The nonreproducibility of numerical experiments on modulated waves is also considered.
Contour detection based on nonlinear discrete diffusion in a cellular nonlinear network
2001
International audience; A contour detection based on a diffusive cellular nonlinear network is proposed. It is shown that there exists a particular nonlinear function for which, numerically, the obtained contour is satisfactory. Furthermore, this nonlinear function can be achieved using analog components.
Compact-like pulse signals in a new nonlinear electrical transmission line
2013
International audience; A nonlinear electrical transmission line with an intersite circuit element acting as a nonlinear resistance is introduced and investigated. In the continuum limit, the dynamics of localized signals is described by a nonlinear evolution equation belonging to the family of nonlinear diffusive Burgers' equations. This equation admits compact pulse solutions and shares some symmetry properties with the Rosenau-Hyman K(2,2) equation. An exact discrete compactly- supported signal voltage is found for the network and the dissipative effects on the pulse motion analytically studied. Numerical simulations confirm the validity of analytical results and the robustness of these …
Cutoff solitons and bistability of the discrete inductance-capacitance electrical line: Theory and experiments
2007
A discrete nonlinear system driven at one end by a periodic excitation of frequency above the upper band edge (the discreteness induced cutoff) is shown to be a means to (1) generate propagating breather excitations in a long chain and (2) reveal the bistable property of a short chain. After detailed numerical verifications, the bistability prediction is demonstrated experimentally on an electrical transmission line made of 18 inductance-capacitance $(LC)$ cells. The numerical simulations of the $LC$-line model allow us also to verify the breather generation prediction with a striking accuracy.
Dissipative lattice model with exact traveling discrete kink-soliton solutions: Discrete breather generation and reaction diffusion regime
1999
International audience; We introduce a nonlinear Klein-Gordon lattice model with specific double-well on-site potential, additional constant external force and dissipation terms, which admits exact discrete kink or traveling wave fronts solutions. In the nondissipative or conservative regime, our numerical simulations show that narrow kinks can propagate freely, and reveal that static or moving discrete breathers, with a finite but long lifetime, can emerge from kink-antikink collisions. In the general dissipative regime, the lifetime of these breathers depends on the importance of the dissipative effects. In the overdamped or diffusive regime, the general equation of motion reduces to a di…
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.
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.
Noise effects on gap wave propagation in a nonlinear discrete LC transmission line
2007
International audience; We report here the results of numerical investigation of noise effects on the propagation in a nonlinear waveguide modeled by a discrete electrical line. Considering a periodic signal of frequency exceeding the natural cutoff frequency of this system, we show that noise can be used to trigger soliton generation in the medium. Besides the classical stochastic resonance signature exhibited by each oscillator of the network, our simulation results reveal in particular that the signal-to-noise ratio remains almost constant in the whole network for an appropriate amount of noise. This interesting feature insures for the generated solitons a quality preserved propagation a…
Theoretical and experimental study of two discrete coupled Nagumo chains
2001
We analyze front wave (kink and antikink) propagation and pattern formation in a system composed of two coupled discrete Nagumo chains using analytical and numerical methods. In the case of homogeneous interaction among the chains, we show the possibility of the effective control on wave propagation. In addition, physical experiments on electrical chains confirm all theoretical behaviors.
PROPAGATING INTERFACES IN A TWO-LAYER BISTABLE NEURAL NETWORK
2006
The dynamics of propagating interfaces in a bistable neural network is investigated. We consider the network composed of two coupled 1D lattices and assume that they interact in a local spatial point (pin contact). The network unit is modeled by the FitzHugh–Nagumo-like system in a bistable oscillator mode. The interfaces describe the transition of the network units from the rest (unexcited) state to the excited state where each unit exhibits periodic sequences of excitation pulses or action potentials. We show how the localized inter-layer interaction provides an "excitatory" or "inhibitory" action to the oscillatory activity. In particular, we describe the interface propagation failure a…
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.
Pinning of a kink in a nonlinear diffusive medium with a geometrical bifurcation: Theory and experiments
2004
International audience; We study the dynamics of a kink propagating in a Nagumo chain presenting a geometrical bifurcation. In the case of weak couplings, we define analytically and numerically the coupling conditions leading to the pinning of the kink at the bifurcation site. Moreover, real experiments using a nonlinear electrical lattice confirm the theoretical and numerical predictions.
Comment on "Dynamics and properties of waves in a modified Noguchi electrical transmission line"
2016
A recent paper [Phys. Rev. E 91, 022925 (2015)PRESCM1539-375510.1103/PhysRevE.91.022925] presents the derivation of the nonlinear equation modeling envelope waves in a specific case of band passed filter discrete nonlinear electrical transmission line (NLTL), called "A modified Noguchi electrical transmission line" according to the authors. Using the reductive perturbation approach in the semidiscrete approximation, they showed that the modulated waves propagating in this NLTL are described by the ordinary nonlinear Schrodinger (NLS) equation. On the basis of their results, the authors claimed that all previous works on the band passed filter NLTL, which considered the vanishing of the dc c…
Experimental nonlinear electrical reaction-diffusion lattice
1998
International audience; A nonlinear electrical reaction-diffusion lattice modelling the Nagumo equation is presented. It is shown that this system supports front propagation with a given velocity. This propagation is observed experimentally using a video acquisition system, and the measured velocity of the front is in perfect agreement with the theoretical prediction.
LONG TIME DYNAMICS OF MODULATED WAVES IN A NONLINEAR DISCRETE LC TRANSMISSION LINE
2003
The long-time dynamics of modulated waves in a nonlinear LC transmission line is investigated. Considering the higher-order nonlinear Schrodinger equation, we define analytically the conditions leading to the instability of modulated waves. We show that two kinds of instabilities may develop in the network depending on the frequency range of the chosen carrier wave and on the magnitude of its initial amplitude, which is confirmed by our numerical simulations. The nonreproducibility of numerical experiments on modulated waves is also considered.
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…
Influence of a nonlinear coupling on the supratransmission effect in modified sine-Gordon and Klein–Gordon lattices
2017
International audience; In this paper, we analyze the conditions leading to the nonlinear supratransmission phenomenon in two different models: a modified fifth order Klein–Gordon system and a modified sine-Gordon system. The modified models considered here are those with mixed coupling, the pure linear coupling being associated with a nonlinear coupling. Especially, we numerically quantify the influence of the nonlinear coupling coefficient on the threshold amplitude which triggers the nonlinear supratransmission phenomenon. Our main result shows that, in both models, when the nonlinear coupling coefficient increases, the threshold amplitude triggering the nonlinear supratransmission pheno…
Generation of nonlinear current-voltage characteristics. A general method
2002
International audience; A general method allowing to construct nonlinear resistors with arbitrary current-voltage (I-V) characteristics is proposed. The example of a cubic I-V characteristic is presented showing a perfect agreement between the theoretical desired resistor and its electronic realization based on analog multipliers.
Noise-enhanced propagation in a dissipative chain of triggers
2002
International audience; We study the influence of spatiotemporal noise on the propagation of square waves in an electrical dissipative chain of triggers. By numerical simulation, we show that noise plays an active role in improving signal transmission. Using the Signal to Noise Ratio at each cell, we estimate the propagation length. It appears that there is an optimum amount of noise that maximizes this length. This specific case of stochastic resonance shows that noise enhances propagation.