Search results for "Nagumo"
showing 10 items of 20 documents
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.
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…
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.
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…
On Some Applications of Nonlinear Differential Equations in Image Processing: Concepts and Electronic Implementation
2011
International audience
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…
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.
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.
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.