0000000001109541
AUTHOR
Jean-marie Bilbault
showing 53 related works from this author
Digital information receiver based on stochastic resonance
2003
International audience; An electronic receiver based on stochastic resonance is presented to rescue subthreshold modulated digital data. In real experiment, it is shown that a complete data restoration is achieved for both uniform and Gaussian white noise.
Polymorphic and regular localized activity structures in a two-dimensional two-component reaction–diffusion lattice with complex threshold excitation
2010
Abstract Space–time dynamics of the system modeling collective behaviour of electrically coupled nonlinear units is investigated. The dynamics of a local cell is described by the FitzHugh–Nagumo system with complex threshold excitation. It is shown that such a system supports formation of two distinct kinds of stable two-dimensional spatially localized moving structures without any external stabilizing actions. These are regular and polymorphic structures. The regular structures preserve their shape and velocity under propagation while the shape and velocity as well as other integral characteristics of polymorphic structures show rather complex temporal behaviour. Both kinds of structures r…
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.
Spiking patterns emerging from wave instabilities in a one-dimensional neural lattice.
2003
The dynamics of a one-dimensional lattice (chain) of electrically coupled neurons modeled by the FitzHugh-Nagumo excitable system with modified nonlinearity is investigated. We have found that for certain conditions the lattice exhibits a countable set of pulselike wave solutions. The analysis of homoclinic and heteroclinic bifurcations is given. Corresponding bifurcation sets have the shapes of spirals twisting to the same center. The appearance of chaotic spiking patterns emerging from wave instabilities is discussed.
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…
Multisite field potential recordings and analysis of the impulse propagation pattern in cardiac cells culture
2007
To provide further insights into the impulse propagation between cardiac myocytes, we performed multiparametric studies of excitation spread with cellular resolution in confluent monolayers of cultured cardiomyocytes (CM). Simultaneous paired intracellular recordings of action potentials in two individual CM revealed slight periodic spontaneous advances/delays in the interspike time lag. Multisite field potential recordings performed with microelectrode arrays (MEA) confirmed random and iterative cycle-to-cycle changes in the direction of excitation spread. These local spontaneous variations in the cardiac impulse propagation pathways may be a safety process protecting against microscopical…
GAP solitons in 1D asymmetric physical systems
2008
We present a general approach for studying the nonlinear transmittance and gap solitons characteristics of asymmetric and one dimensional (1 D) systems in the low amplitude or Nonlinear Schrodinger limit. Included in this approach are some novel results on naturally asymmetric systems and systems where the symmetry is broken by an external constant force.
Mise en œuvre d’une chaîne d’acquisition et de traitement du signal : Application à la mesure du rythme cardiaque en licence 1ère année
2014
International audience; Dans le cadre de cet article, nous présentons un projet de travaux pratiques mis en place dans le cadre d’un module intitulé « Sciences et Traitement de l’Information ». L’objectif pédagogique de ce module est de donner aux étudiants de 1ère année de Licence un aperçu applicatif de l’électronique, du traitement du signal et de l’informatique. Cette découverte se fait au travers de la réalisation d’un système d’acquisition et de traitement, ce projet étant découpé en fonctions de base qui sont étudiées d’abord séparément avant d’être regroupées pour aboutir à une application réelle. La mise en place de ce module date de la rentrée 2012-2013 et le retour d’expérience m…
Experimental study of low-voltage surge protection device response in realistic systems
2008
Experimental results on low-voltage surge protection under fast pulses in realistic wiring systems are presented. A fast voltage pulse generator is designed to provide fast voltage pulses with short steep fronts. The effective residual voltage of protected equipment is then investigated and compared with simulation results.
Experimental study of electrical FitzHugh-Nagumo neurons with modified excitability
2006
International audience; We present an electronical circuit modelling a FitzHugh-Nagumo neuron with a modified excitability. To characterize this basic cell, the bifurcation curves between stability with excitation threshold, bistability and oscillations are investigated. An electrical circuit is then proposed to realize a unidirectional coupling between two cells, mimicking an inter-neuron synaptic coupling. In such a master-slave configuration, we show experimentally how the coupling strength controls the dynamics of the slave neuron, leading to frequency locking, chaotic behavior and synchronization. These phenomena are then studied by phase map analysis. The architecture of a possible ne…
COMPRESSION OF ENVELOPE SOLITONS IN NONLINEAR ELECTRICAL LINES
1989
Resume : La propagation des solitons enveloppe dans les lignes non lineaires de transmission electrique et de transmission Josephson est etudiee sous l'aspect theorique et en simulation numerique. Dans l'approximation des milieux continus et la limite des faibles amplitudes, les equations caracteristiques de ces lignes se ramenent a l'equation NLS . La solution "a deux solitons enveloppe" se propage parfaitement dans les lignes considerees avec des phenomenes de recurrence et de compression d'enveloppe. Ceci est observe egalement pour des profils d'excitation non solution de NLS, ce qui est d'un grand interet pour les applications pratiques.
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.
Anharmonic effects on the dynamic behavior’s of Klein Gordon model’s
2021
Abstract This work completes and extends the Ref. Tchakoutio Nguetcho et al. (2017), in which we have focused our attention only on the dynamic behavior of gap soliton solutions of the anharmonic Klein-Gordon model immersed in a parameterized on-site substrate potential. We expand our work now inside the permissible frequency band. These considerations have crucial effects on the response of nonlinear excitations that can propagate along this model. Moreover, working in the allowed frequency band is not only interesting from a physical point of view, it also provides an extraordinary mathematical model, a new class of differential equations possessing vital parameters and vertical singular …
Nonlinear mechanics of DNA doule strand: existence of the compact-envelope bright solitary wave
2013
We study the nonlinear dynamics of a homogeneous DNA chain which is based on site-dependent finite stacking and pairing enthalpies. We introduce an extended nonlinear Schrödinger equation describing the dynamics of modulated wave in DNA model. We obtain envelope bright solitary waves with compact support as a solution. Analytical criteria of existence of this solution are derived. The stability of bright compactons is confirmed by numerical simulations of the exact equations of the lattice. The impact of the finite stacking energy is investigated and we show that some of these compact bright solitary waves are robust, while others decompose very quickly depending on the finite stacking para…
STATISTICAL MECHANICS OF NONCLASSIC SOLITONIC STRUCTURES-BEARING DNA SYSTEM
2011
We theoretically investigate the thermodynamic properties of modified oscillator chain proposed by Peyrard and Bishop. This model obtained by adding the quartic anharmonicity term to the coupling in the Peyrard–Bishop model is useful to model the coexistence of various phases of the molecule during the denaturation phenomenon. Within the model, the negative anharmonicity is responsible for the sharpness of calculated melting curves. We perform the transfer integral calculations to demonstrate that the model leads to a good agreement with known experimental results for DNA.
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.
Spiral wave induced numerically using electrical stimulation and comparison with experimental results.
2010
Experiments in vitro on a Microelectrode Array (MEA) platform show that electrical stimulation can provoke the generation of spiral waves in cardiac tissue. Nevertheless, the conditions leading to this artificial fibrillation state remain unclear. In order to have a better understanding of this phenomenon, a numerical simulation study has been conducted. The results obtained with a two-dimensional FitzHugh-Nagumo model proved that it is possible to create spiral waves by adding a stimulation current under certain conditions, which are made explicit.
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.
Reaction-Diffusion Network For Geometric Multiscale High Speed Image Processing
2010
International audience; In the framework of heavy mid-level processing for high speed imaging, a nonlinear bi-dimensional network is proposed, allowing the implementation of active curve algorithms. Usually this efficient type of algorithm is prohibitive for real-time image processing due to its calculus charge and the inadequate structure for the use of serial or parallel architectures. Another kind of implementation philosophy is proposed here, by considering the active curve generated by a propagation phenomenon inspired from biological modeling. A programmable nonlinear reaction-diffusion system is proposed under front control and technological constraints. Geometric multiscale processin…
A hybrid stimulation strategy for suppression of spiral waves in cardiac tissue
2011
International audience; Atrial fibrillation (AF) is the most common cardiac arrhythmia whose mechanisms are thought to be mainly due to the self perpetuation of spiral waves (SW). To date, available treatment strategies (antiarrhythmic drugs, radiofrequency ablation of the substrate, electrical cardioversion) to restore and to maintain a normal sinus rhythm have limitations and are associated with AF recurrences. The aim of this study was to assess a way of suppressing SW by applying multifocal electrical stimulations in a simulated cardiac tissue using a 2D FitzHugh-Nagumo model specially convenient for AF investigations. We identified stimulation parameters for successful termination of S…
3-D shape reconstruction in an active stereo vision system using genetic algorithms
2003
Abstract The recovery of 3-D shape information (depth) using stereo vision analysis is one of the major areas in computer vision and has given rise to a great deal of literature in the recent past. The widely known stereo vision methods are the passive stereo vision approaches that use two cameras. Obtaining 3-D information involves the identification of the corresponding 2-D points between left and right images. Most existing methods tackle this matching task from singular points, i.e. finding points in both image planes with more or less the same neighborhood characteristics. One key problem we have to solve is that we are on the first instance unable to know a priori whether a point in t…
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.
Modulational instability and critical regime in a highly birefringent fiber
1996
We report experimental observations of modulational instability of copropagating waves in a highly birefringent fiber for the normal dispersion regime. We first investigate carefully the system behavior by means of nonlinear Schr\"odinger equations and phase-matching conditions, and then, experimentally, we use two distinct techniques for observing MI (modulational instability) in the fiber; namely, the single-frequency copropagation, where two pump waves of identical frequency copropagate with orthogonal polarizations parallel to the two birefringence axes of the fiber, and the two-frequency copropagation, where the two polarized waves copropagate with different frequencies. In both cases …
Compact-envelope bright solitary wave in a DNA double strand
2012
International audience; We study the nonlinear dynamics of a homogeneous DNA chain which is based on site-dependent finite stacking and pairing enthalpies. We introduce an extended nonlinear Schroedinger equation describing the dynamics of modulated waves in DNA model. We obtain envelope bright solitary waves with compact support as a solution. Analytical criteria of existence and stability of this solution are derived. The stability of bright compactons is confirmed by numerical simulations of the exact equations of the lattice. The impact of the fi nite stacking energy is investigated and we show that some of these compact bright solitary waves are very robust, while others decompose quic…
A theoretical approach of the propagation through geometrical constraints in cardiac tissue
2007
International audience; The behaviour of impulse propagation in the presence of non-excitable scars and boundaries is a complex phenomenon and induces pathological consequences in cardiac tissue. In this article, a geometrical con¯guration is considered so that cardiac waves propagate through a thin strand, which is connected to a large mass of cells. At this interface, waves can slow down or even be blocked depending on the width of the strand. We present an analytical approach leading to determine the blockade condition, by introducing planar travelling wavefront and circular stationary wave. Eventually, the in°uence of the tissue geometry is examined on the impulse propagation velocity.
Behavior of gap solitons in anharmonic lattices
2017
International audience; Using the theory of bifurcation, we provide and find gap soliton dynamics in a nonlinear Klein-Gordon model with anharmonic, cubic, and quartic interactions immersed in a parametrized on-site substrate potential. The case of a deformable substrate potential allows theoretical adaptation of the model to various physical situations. Nonconvex interactions in lattice systems lead to a number of interesting phenomena that cannot be produced with linear coupling alone. By investigating the dynamical behavior and bifurcations of solutions of the planar dynamical systems, we derive a variety of exotic solutions corresponding to the phase trajectories under different paramet…
EMERGENCE OF TRAVELLING WAVES IN SMOOTH NERVE FIBRES
2008
International audience; An approximate analytical solution characterizing initial condi- tions leading to action potential ¯ring in smooth nerve ¯bres is determined, using the bistable equation. In the ¯rst place, we present a non-trivial sta- tionary solution wave. Then, we extract the main features of this solution to obtain a frontier condition between the initiation of the travelling waves and a decay to the resting state. This frontier corresponds to a separatrix in the projected dynamics diagram depending on the width and the amplitude of the stationary wave.
Analysis of an Experimental Model of In Vitro Cardiac Tissue Using Phase Space Reconstruction
2014
International audience; The in vitro cultures of cardiac cells represent valuable models to study the mechanism of the arrhythmias at the cellular level. But the dynamics of these experimental models cannot be characterized precisely, as they include a lot of parameters that depend on experimental conditions. This paper is devoted to the investigation of the dynamics of an in vitro model using a phase space reconstruction. Our model, based on the heart cells of new born rats, generates electrical field potentials acquired using a microelectrode technology, which are analyzed in normal and under external stimulation conditions. Phase space reconstructions of electrical field potential signal…
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…
Cardiac arrhythmias induced by an electrical stimulation at a cellular level
2008
To provide insights into the impulse propagation between cardiac myocytes, we performed studies of excitation spread with cellular resolution in confluent monolayers of cultured cardiomyocytes (CM). Multisite field potentials have been recorded using microelectrode arrays (MEA) technology in a basal condition and in proarrhythmic conditions induced by a high frequency electrical stimulation. The in vitro observation of spiral waves opens a new way to test the anti-arrhythmic drugs or strategies at cellular level.
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 …
Gap solitons in nonlinear electrical transmission lines
2005
We study theoretically and numerically the properties of monochromatic waves in a nonlinear electrical transmission line,whose capacitance has a periodic spatial variation.ln the continuum limit and weak amplitude limit we reduce the characteristic equations of this system to NLS equation. We find analytical solutions for the voltage envelope, which propagate with frequency in the gap induced by the capacitance periodicity. Our numerical experiments show that, when the input voltage increases, the transmissivity in the gap increases and the voltage envelope approaches the stationnary shape predicted by theory.
Heteroclinic contours and self-replicated solitary waves in a reaction–diffusion lattice with complex threshold excitation
2008
Abstract The space–time dynamics of the network system modeling collective behavior of electrically coupled nonlinear cells is investigated. The dynamics of a local cell is described by the FitzHugh–Nagumo system with complex threshold excitation. Heteroclinic orbits defining traveling wave front solutions are investigated in a moving frame system. A heteroclinic contour formed by separatrix manifolds of two saddle-foci is found in the phase space. The existence of such structure indicates the appearance of complex wave patterns in the network. Such solutions have been confirmed and analyzed numerically. Complex homoclinic orbits found in the neighborhood of the heteroclinic contour define …
Bifurcations of phase portraits of a Singular Nonlinear Equation of the Second Class
2014
Abstract The soliton dynamics is studied using the Frenkel Kontorova (FK) model with non-convex interparticle interactions immersed in a parameterized on-site substrate potential. The case of a deformable substrate potential allows theoretical adaptation of the model to various physical situations. Non-convex interactions in lattice systems lead to a number of interesting phenomena that cannot be produced with linear coupling alone. In the continuum limit for such a model, the particles are governed by a Singular Nonlinear Equation of the Second Class. The dynamical behavior of traveling wave solutions is studied by using the theory of bifurcations of dynamical systems. Under different para…
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.
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.
Anti-phase wave patterns in a ring of electrically coupled oscillatory neurons
2013
International audience; Space-time dynamics of the network system modeling collective behavior of electrically coupled nonlinear cells is investigated. The dynamics of a local cell is described by the dimensionless Morris-Lecar system. It is shown that such a system yields a special class of traveling localized collective activity so called "anti-phase wave patterns". The mechanisms of formation of the patterns are discussed and the region of their existence is obtained by using the weakly coupled oscillators theory.
<title>Reaction-diffusion electrical network for image processing</title>
2006
We consider an experimental setup, modelling the FitzHugh-Nagumo equation without recovery term and composed of a 1D nonlinear electrical network made up of discrete bistable cells, resistively coupled. In the first place, we study the propagation of topological fronts in the continuum limit, then in more discrete case. We propose to apply these results to the domain of signal processing. We show that erosion and dilation of a binary signal, can be obtained. Finally, we extend the study to 2D lattices and show that it can be of great interest in image processing techniques.© (2006) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted fo…
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.
Experimental study of bifurcations in modified FitzHugh-Nagumo cell
2003
A nonlinear electrical circuit is proposed as a basic cell for modelling the FitzHugh-Nagumo equation with a modified excitability. Depending on initial conditions and parameters, experiments show various dynamics including stability with excitation threshold, bistability and oscillations.
Détection d'Anomalie dans les Signaux Physiologiques
2015
International audience; Les signaux physiologiques sont des séries temporelles riches en informations. Analyser ces signaux pour extraire ces informations, pour établir un diagnostic ou encore pour prédire une évolution, nécessite des outils performants et adaptés à leurs caractéristiques intrinsèques. En effet le comportement d'un système biologique dépend des variations de très nombreux paramètres, ce qui le rend alors presque imprévisible. Les méthodes issues de la théorie du chaos et de la dynamique non linéaire apportent des éléments qui permettent de comprendre ce type de comportements, et d'établir ainsi un lien qualitatif avec des modèles mathématiques bio-inspirés ou phénoménologiq…
Phase Space Reconstruction of an Experimental Cardiac Electrical Signal
2014
International audience; Cardiac arrhythmias are very common pathologies which can be treated either by medications, invasive ablation procedures or device implantations. In order to improve theses treatments, clinical and experimental models are used to test new drugs. In this context, in vitro cultures of cardiac cells represent valuable models to study the mechanism of the arrhythmias at the cellular level. In this paper, we investigate the stability and robustness of an experimental model in normal and under external stimulation conditions. Phase space reconstructions of attractors in normal and arrhythmic cases are performed after characterizing the nonlinearity of the model, computing …
Active spike transmission in the neuron model with a winding threshold manifold
2012
International audience; We analyze spiking responses of excitable neuron model with a winding threshold manifold on a pulse stimulation. The model is stimulated with external pulse stimuli and can generate nonlinear integrate-and-fire and resonant responses typical for excitable neuronal cells (all-or-none). In addition we show that for certain parameter range there is a possibility to trigger a spiking sequence with a finite number of spikes (a spiking message) in the response on a short stimulus pulse. So active transformation of N incoming pulses to M (with M>N) outgoing spikes is possible. At the level of single neuron computations such property can provide an active "spike source" comp…
Modulational stability brought by cubic–quartic interactions of the nearest-neighbor in FK model subjected in a parametrized on-site potential
2022
Abstract This work extends to higher-order interactions the results of Ref. Nguetcho (2021), in which we discussed only on modulational instability in one-dimensional chain made of atoms, harmonically coupled to their nearest neighbors and subjected to an external on-site potential. Here we investigate the competition between cubic-quartic nonlinearities interactions of the nearest-neighbor and substrate’s deformability, and mainly discuss its impact on the modulational instability of the system. This makes it possible to adapt the theoretical model to a real physical system such as atomic chains or DNA lattices. The governing equation, derived from the modified Frenkel-Kontorova model, is …
ANALYTICAL DETERMINATION OF INITIAL CONDITIONS LEADING TO FIRING IN NERVE FIBERS
2007
International audience; An analytical solution characterizing initial conditions leading to action potential firing in smooth nerve fibers is determined, using the bistable equation. In the first place, we present a nontrivial stationary solution wave, then, using the perturbative method, we analyze the stability of this stationary wave. We show that it corresponds to a frontier between the initiation of the travelling waves and a decay to the resting state. Eventually, this analytical approach is extended to FitzHugh-Nagumo model.
EXPERIMENTAL PROPAGATION FAILURE IN A NONLINEAR ELECTRICAL LATTICE
2004
We consider an experimental setup, modeling the FitzHugh–Nagumo equation without recovery term and composed of a nonlinear electrical network made up of discrete bistable cells, resistively coupled. In the first place, we study experimentally the propagation of topological fronts in the continuum limit where the analytical solution can be obtained. We show that experimental results match the theoretical predictions. The discrete case is then investigated theoretically and in the lattice, emphasizing the pinning of traveling waves.
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.
Active spike responses of analog electrical neuron: Theory and experiments
2010
Using an analog electrical FitzHugh-Nagumo neuron including complex threshold excitation (CTE) properties, we analyze its spiking responses under pulse stimulation corresponding to oscillating threshold manifold. The system is subjected to outside pulse stimulus and can generate nonlinear integrate-and-flre and resonant responses which are typical for excitable neuronal cells ("all-or-none"). The answer of the neuron strongly depends on the number and the characteristics of incoming impulses (amplitude, width, strength and frequency). For certain parameters range, there is a possibility to trigger a spiking sequence with a finite number of spikes in response of a single short stimulus pulse…
Statistical mechanics of nonclassic solitonic structures-bearing dna system
2011
International audience
Vibrational Resonance in inhomogeneous and space-dependent nonlinear damped systems
2020
International audience; The properties of nonlinear systems have attracted a considerable interest these past years since they can be used to develop bio-inspired applications ranging from signal detection to image processing. Among these nonlinear signatures is Vibrational Resonance (V.R.) which expresses the ability of a nonlinear system to take benefit of a high frequency perturbation in order to enhance its response to a weak low frequency excitation . Since its introduction in mechanical systems and electronic devices, this effect has been widely reported in various systems and for different applications. Indeed, V.R can be used to detect subthreshold signals or to enhance the percepti…
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.
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…