This paper gives asymptotic approximations for the probability density functions for delay bifurcations altered by noise. In these processes, very small noise signi cantly reduces the delay until the transition time. The asymptotic approximation describes the dynamics through the transition and is used to calculate mean transition times. The method is applied to a one dimensional canonical mode...

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...

A new technique is used to reduce the classic Hodgkin-Huxley model to a two-dimensional neuronal model which retains the essential features of the full description. The resulting equations are similar in spirit to those of the FitzHugh-Nagumo model, but they exhibit some essential diierences which provide a more accurate representation of the full dynamics. By further simplifying the two-dimens...

We consider a network of reaction diffusion systems of generalized FitzHugh-Nagumo type, where the cubic function is replaced by a polynomial function with odd degree. We deal with asymptotic behaviour and synchronization of the whole network. These results extend a previous work in which we considered particular systems of FitzHugh Nagumo type.

In the study, the activation propagation velocity in cardiac tissue was simulated in COMSOL Multiphysics environment using the modified FitzHugh-Nagumo model of the electrical excitation. The influence of different model parameters and stimulation conditions on the activation propagation velocity was evaluated. The homogeneous slab model was used as the model of the atrial wall. Results of simu...

We study Hopf bifurcation solutions to the Monodomain model equipped with FitzHughNagumo cell dynamics. This reaction-diffusion system plays an important role in the field of electrocardiology as a tractable mathematical model of the electrical activity in the human heart. In our setting the bounded spatial domain consists of two subdomains: a collection of automatic cells surrounded by collect...

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 ...

Abstract We consider the existence and first order conditions of optimality for a stochastic optimal control problem inspired by celebrated FitzHugh–Nagumo model, with nonlinear diffusion term, perturbed linear multiplicative Brownian-type noise. The main novelty present paper relies on application rescaling method which allows us to reduce original random one.

The work concerns the multiscale modeling of a nerve fascicle myelinated axons. We present rigorous derivation macroscopic bidomain model describing behavior electric potential in based on FitzHugh–Nagumo membrane dynamics. approach is two-scale convergence machinery combined with method monotone operators.