For a linearized version of the FitzHugh–Nagumo model, firing and resetting conditions are defined by analogy with the Integrate and Fire model. The dynamical behavior of the model, subject to periodic synaptic inputs, is investigated both theoretically and numerically, with particular emphasis on the synchronization properties. The study is then extended to a network of two synaptically couple...

Abstract We will introduce numerical methods for systems of ODEs by considering the celebrated FitzHugh-Nagumo model published FitzHugh [1] in 1961 and, independently, Nagumo et. al. [2] 1962. The is a system ordinary differential equations with two unknowns, and commonly used as simple action potentials excitable pacemaker cells.

This paper describes the identification of a temperature dependent FitzHugh–Nagumo model directly from experimental observations with controlled inputs. By studying the steady states and the trajectory of the phase of the variables, the stability of the model is analyzed and a rule to generate oscillation waves is proposed. The dependence of the oscillation frequency and propagation speed on th...

We consider the problem of reconstructing chaotic attractors from spike trains produced by model neurons. We nd that the period/parameter plot, which displays the dependence of the oscillation frequency of the spiking model on the input level, is a useful device for determining the success of reconstruction. A new three-dimensional version of Fitzhugh-Nagumo spiking dynamics is investigated alo...

In this work we describe experimental results regarding an optoelectronic implementation of a dynamic neuron model. The model is a variation of the FitzHugh-Nagumo equations, and it is implemented with linear optics and simple linear electronic feedback. The demonstration of dynamic features of the isolated neuron and of optical coupling between neurons is discussed, as well as the computationa...

Study of neurons plays a key role in the fields of basic and medical research aiming at the development of electrically active implants. The Fitzhugh-Nagumo equations are used to model and simulate the spike generation and propagation in a squid giant axon using Comsol Multiphysics® 3.5a Software. It is shown that the Fitzhugh-Nagumo equations allow for a geometrical explanation of important bi...

The Fitzhugh-Nagumo (fn) mathematical model characterizes the action potential of the membrane. The dynamics of the Fitzhugh-Nagumo model have been extensively studied both with a view to their biological implications and as a test bed for numerical methods, which can be applied to more complex models. This paper deals with the dynamics in the (FH) model. Here, the dynamics are analyzed, qualit...

We employed Poincaré return mappings for a parameter interval to an exemplary elliptic bursting model, the FitzHugh-Nagumo-Rinzel model. Using the interval mappings, we were able to examine in detail the bifurcations that underlie the complex activity transitions between: tonic spiking and bursting, bursting and mixed-mode oscillations, and finally, mixed-mode oscillations and quiescence in the...