We consider a nonlinear reaction diffusion system of parabolic type known as the monodomain equations, which model interaction electric current in cell. Together with FitzHugh-Nagumo for nonlinearity they represent defibrillation processes human heart. study fairly general co-located inputs and outputs describing both boundary distributed control observation. The objective is output trajectory ...

Trigger waves are a recurring biological phenomenon involved in transmitting information quickly and reliably over large distances. Well-characterized examples include action potentials propagating along the axon of a neuron, calcium waves in various tissues, and mitotic waves in Xenopus eggs. Here we use the FitzHugh-Nagumo model, a simple model inspired by the action potential that is widely ...

A FitzHugh–Nagumo type spiking neuron model equipped with an asymmetric activation function is investigated. An analogue nonlinear electrical circuit imitating the dynamics of the model is proposed. It is demonstrated that a simple first order linear filter coupled to the system can inhibit spiking and stabilize the system on an unstable steady state, the position of which is not required to be...

In this paper we adopt a temporal coding approach to neuronal modeling of the visual cortex, using oscillations. We propose a hierarchy of three processing modules corresponding to di erent levels of representation. The rst layer encodes the input image (stimulus) into an array of units, while the second layer consists of a network of FitzHugh-Nagumo oscillators. The dynamical behaviour of the ...

With a modulated CO2 laser as a standard model of periodically driven multistable systems, we experimentally demonstrate that a small-amplitude optoelectronic feedback perturbation can efficiently transform a bursting chaotic system to a nonchaotic one. Numerical simulations are in excellent agreement with the experimental results. The control has also been equally effective in the case of a dr...

We investigate the effects of cross-diffusion on propagating waves in an activator-inhibitor system. The model consists of a piecewise linear approximation of FitzHugh-Nagumo kinetics and a cross-diffusion term for either the activator or the inhibitor. We obtain exact analytic solutions for traveling fronts and solitary pulses and discuss the corresponding speed diagrams. A detailed comparison...

The aim of this work is to describe the dynamics a discrete fractional-order reaction–diffusion FitzHugh–Nagumo model. We established acceptable requirements for local asymptotic stability system’s unique equilibrium. Moreover, we employed Lyapunov functional show that constant equilibrium solution globally asymptotically stable. Furthermore, numerical simulations are shown clarify and exemplif...

An optoelectronic implementation of a spiking neuron model based on the FitzHugh-Nagumo equations is presented. A tunable semiconductor laser source and a spectral filter provide a nonlinear mapping from driver voltage to detected signal. Linear electronic feedback completes the implementation, which allows either electronic or optical input signals. Experimental results for a single system and...

We consider the problem of how to recover the state and parameter values of typical model neurons, such as Hindmarsh-Rose, FitzHugh-Nagumo, Morris-Lecar, from in-vitro measurements of membrane potentials. In control theory, in terms of observer design, model neurons qualify as locally observable. However, unlike most models traditionally addressed in control theory, no parameter-independent dif...

The variability and mean of the firing rate of Hodgkin-Huxley and FitzHugh-Nagumo neurons subjected to random synaptic input are only weakly dependent on the level of inhibitory input, unlike integrate-and-fire neurons. For the latter model, substantial inhibitory input is essential to ensure output variability close to Poissonian firing. It cannot therefore be used routinely in stochastic netw...