Search results for "FitzHugh-Nagumo"

Memristors in Nonlinear Network : Application to Information (Signal and Image) Processing

2021

Memristor is a two-terminal nonlinear dynamic electronic device. Typically, it is a passive nano-device whose conductivity is controlled by the flux, time-integral of the voltage across its terminals, or by the charge, time-integral of the current flowing through it, and it presents interesting features for versatile applications. This thesis considers memristor use as a neighborhood connection for 2D cellular nonlinear or neural network (CNN), essentially for information (image and signal) processing and electronic prosthesis. We develop a model of the memristor based 2D cellular nonlinear networks CNNs compatible to image applications by incorporating memristor in the adjacent neighborhoo…

Cross-diffusion effects on stationary pattern formation in the FitzHugh-Nagumo model

2022

<p style='text-indent:20px;'>We investigate the formation of stationary patterns in the FitzHugh-Nagumo reaction-diffusion system with linear cross-diffusion terms. We focus our analysis on the effects of cross-diffusion on the Turing mechanism. Linear stability analysis indicates that positive values of the inhibitor cross-diffusion enlarge the region in the parameter space where a Turing instability is excited. A sufficiently large cross-diffusion coefficient of the inhibitor removes the requirement imposed by the classical Turing mechanism that the inhibitor must diffuse faster than the activator. In an extended region of the parameter space a new phenomenon occurs, namely the exis…

Influence of noise sources on FitzHugh-Nagumo model in suprathreshold regime

2005

We study the response time of a neuron in the transient regime of FitzHugh-Nagumo model, in the presence of a suprathreshold signal and noise sources. In the deterministic regime we find that the activation time of the neuron has a minimum as a function of the signal driving frequency. In the stochastic regime we consider two cases: (a) the fast variable of the model is noisy, and (b) the slow variable, that is the recovery variable, is subjected to fluctuations. In both cases we find two noise-induced effects, namely the resonant activation-like and the noise enhanced stability phenomena. The role of these noise-induced effects is analyzed. The first one produces suppression of noises, whi…

Suppression of noise in Fitzhugh-Nagumo model driven by a strong periodic signal

2005

Noise contribution to resonance phenomena and information propagation in non linear electronic networks

2015

This manuscript presents research aiming to show possible positive effects of deterministic and stochastic perturbations on the responses of different nonlinear systems. To that end, both numerical and experimental studies were carried out on two kinds of structures : an elementary electronic FitzHugh-Nagumo oscillator and an electrical line developed by resistively coupling 45 elementary cells. In the first section, the elementary cell characterization was undertaken in a deterministic regime. In the presence of a bichromatic stimulus, it is shown that when the low frequency component is subthreshold, its detection can be maximized for an optimal magnitude of the second component thanks to…

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.

Electronic implementation of a non-linear oscillator subjected to noise : application to the modeling of neuronal information coding

2011

We study the nonlinear FitzHugh-Nagumo model witch describes the dynamics of excitable neural element. It is well known that this system exhibits three different possible responses. Indeed, the system can be mono-stable, oscillatory or bistable. In the oscillatory regime, the system periodically responds by generating action potential. By contrast, in the mono-stable state the system response remains constant after a transient. Under certain conditions, the system can undergo a bifurcation between the stable and the oscillatory regime via the so called Andronov-Hopf bifurcation. In this Phd thesis, we consider the FitzHugh-Nagumo model in the stable state, that is set near the Andronov-Hopf…