Search results for "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

Spatially localized solutions of the Hammerstein equation with sigmoid type of nonlinearity

2016

Abstract We study the existence of fixed points to a parameterized Hammerstein operator H β , β ∈ ( 0 , ∞ ] , with sigmoid type of nonlinearity. The parameter β ∞ indicates the steepness of the slope of a nonlinear smooth sigmoid function and the limit case β = ∞ corresponds to a discontinuous unit step function. We prove that spatially localized solutions to the fixed point problem for large β exist and can be approximated by the fixed points of H ∞ . These results are of a high importance in biological applications where one often approximates the smooth sigmoid by discontinuous unit step function. Moreover, in order to achieve even better approximation than a solution of the limit proble…

Parameters analysis of FitzHugh-Nagumo model for a reliable simulation

2014

International audience; Derived from the pioneer ionic Hodgkin-Huxley model and due to its simplicity and richness from a point view of nonlinear dynamics, the FitzHugh-Nagumo model has been one of the most successful neuron / cardiac cell model. It exists many variations of the original FHN model. Though these FHN type models help to enrich the dynamics of the FHN model. The parameters used in these models are often in biased conditions. The related results would be questionable. So, in this study, the aim is to find the parameter thresholds for one of the commonly used FHN model in order to pride a better simulation environment. The results showed at first that inappropriate time step and…

Dynamics of a FitzHugh-Nagumo system subjected to autocorrelated noise

2008

We analyze the dynamics of the FitzHugh-Nagumo (FHN) model in the presence of colored noise and a periodic signal. Two cases are considered: (i) the dynamics of the membrane potential is affected by the noise, (ii) the slow dynamics of the recovery variable is subject to noise. We investigate the role of the colored noise on the neuron dynamics by the mean response time (MRT) of the neuron. We find meaningful modifications of the resonant activation (RA) and noise enhanced stability (NES) phenomena due to the correlation time of the noise. For strongly correlated noise we observe suppression of NES effect and persistence of RA phenomenon, with an efficiency enhancement of the neuronal respo…

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.

Suppression of noise in FitzHugh–Nagumo model driven by a strong periodic signal

2005

Abstract The response time of a neuron in the presence of a strong periodic driving in the stochastic FitzHugh–Nagumo model is investigated. We analyze two cases: (i) the variable that corresponds to membrane potential is subjected to fluctuations, and (ii) the recovery variable associated with the refractory properties of a neuron is noisy. The influence of noise sources on the delay of the response of a neuron is analyzed. In both cases we observe a resonant activation-like phenomenon and suppression of noise: the negative effect of fluctuations on the process of spike generation is minimal near the resonance region. The phenomenon of noise enhanced stability is also observed in both case…

Pattern selection in the 2D FitzHugh–Nagumo model

2018

We construct square and target patterns solutions of the FitzHugh–Nagumo reaction–diffusion system on planar bounded domains. We study the existence and stability of stationary square and super-square patterns by performing a close to equilibrium asymptotic weakly nonlinear expansion: the emergence of these patterns is shown to occur when the bifurcation takes place through a multiplicity-two eigenvalue without resonance. The system is also shown to support the formation of axisymmetric target patterns whose amplitude equation is derived close to the bifurcation threshold. We present several numerical simulations validating the theoretical results.