Search results for " Nonlinear"
showing 10 items of 1224 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.
COLORED NOISE EFFECTS ON GHOST STOCHASTIC RESONANCE
2014
International audience; We analyze the Ghost Stochastic Resonance (GSR) effect in an electronic circuit exactly ruled by the FitzHugh-Nagumo (FHN) equations, both numerically and experimentally. When the circuit is excited with a bichromatic driving with two close frequencies, we show that for an appropriate noise intensity the circuit response exhibits a ghost frequency which is not present in the biharmonic input signal. In this paper, we highlight the e ects of colored noise on GSR.
A comparative study of noise effects in a FitzHugh-Nagumo circuit
2014
International audience; This paper focuses on the behaviour of a nonlinear FitzHugh-Nagumo circuit in the stochastic case that is in presence of noise and without deterministic driving. When the circuit is tuned below the Andronov-Hopf bifurcation, classical coherence res- onance signature is revealed. We compare the stochastic response of the system when the noise acts on two different parameters of the system. It is experimentally shown that an enhancement of the systems response can be achieved when the noise is directly added into the nonlinearity.
Predictive Chaos Control for the 1D-map of Action Potential Duration
2016
International audience; In the present work, a nonlinear control method namely predictive controlis investigated. The proposed method allows stabilizing unstable period-1 rhythm.Using mathematical analysis and computer simulations, we show that this methodcan be used to control chaotic behavior or pathological rhythms. As example, theresults are illustrated in the case of the 1D-map action potential duration (APDi+1)which modelizes the cardiac action potential duration as the function of the previousone (APDi).
Computational approach to compact Riemann surfaces
2017
International audience; A purely numerical approach to compact Riemann surfaces starting from plane algebraic curves is presented. The critical points of the algebraic curve are computed via a two-dimensional Newton iteration. The starting values for this iteration are obtained from the resultants with respect to both coordinates of the algebraic curve and a suitable pairing of their zeros. A set of generators of the fundamental group for the complement of these critical points in the complex plane is constructed from circles around these points and connecting lines obtained from a minimal spanning tree. The monodromies are computed by solving the defining equation of the algebraic curve on…
Rotation Forms and Local Hamiltonian Monodromy
2017
International audience; The monodromy of torus bundles associated with completely integrable systems can be computed using geometric techniques (constructing homology cycles) or analytic arguments (computing discontinuities of abelian integrals). In this article, we give a general approach to the computation of monodromy that resembles the analytical one, reducing the problem to the computation of residues of polar 1-forms. We apply our technique to three celebrated examples of systems with monodromy (the champagne bottle, the spherical pendulum, the hydrogen atom) and to the case of non-degenerate focus-focus singularities, re-obtaining the classical results. An advantage of this approach …
The tennis racket effect in a three-dimensional rigid body
2017
We propose a complete theoretical description of the tennis racket effect, which occurs in the free rotation of a three-dimensional rigid body. This effect is characterized by a flip ($\pi$- rotation) of the head of the racket when a full ($2\pi$) rotation around the unstable inertia axis is considered. We describe the asymptotics of the phenomenon and conclude about the robustness of this effect with respect to the values of the moments of inertia and the initial conditions of the dynamics. This shows the generality of this geometric property which can be found in a variety of rigid bodies. A simple analytical formula is derived to estimate the twisting effect in the general case. Differen…
Modélisation, Analyse et Traitement de l'Information
2016
Mes activités de recherche s’articulent, d’une part, autour de l’instrumentation et du génie biomédical,et, d’autre part, autour du traitement et de la transmission non linéaire de l’information. Elles sebasent sur la modélisation des signaux à partir de modèles non linéaires (principalement modèles deréaction-diffusion. . . ) continus (EDP) et discrets (numériques). Dans cette partie, d’un point de vuefondamental, des phénomènes dynamiques complexes ou chaotiques sont caractérisés à travers l’analyse,la classification, la reconnaissance des motifs dans des signaux physiologiques ou issus des circuitsélectroniques. Un autre axe sur lequel je travaille concerne l’analyse et le traitement des…
Fractal Weyl law for open quantum chaotic maps
2014
We study the semiclassical quantization of Poincar\'e maps arising in scattering problems with fractal hyperbolic trapped sets. The main application is the proof of a fractal Weyl upper bound for the number of resonances/scattering poles in small domains near the real axis. This result encompasses the case of several convex (hard) obstacles satisfying a no-eclipse condition.
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.