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 research paper, an improved Chebyshev-Gauss-Lobatto pseudospectral approximation of nonlinear Burger-Huxley and Fitzhugh- Nagumo equations have been presented. The method employs chebyshev Gauss-Labatto points in time and space to obtain spectral accuracy. The mapping has introduced and transformed the initial-boundary value non-homogeneous problem to homogeneous problem. The main probl...

FitzHugh-Nagumo (FHN) model is a famous Reaction-Diffusion System which first introduced for the conduction of electrical impulses along a nerve fiber. This model is also considered as an abstract model for pattern formation. Here, we have used the Cellular Automata method to simulate the pattern formation of the FHN model. It is shown that the pattern of this model is very similar to those...

Chaos is an important applied area in nonlinear dynamical systems and it is applicable to many real-world systems including the biological systems. Nerve membranes are known to exhibit their own nonlinear dynamics which generate and propagate action potentials. Such nonlinear dynamics in nerve membranes can produce chaos in neurons and related bifurcations. In 1952, A.L. Hodgkin and A.F. Huxley...

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...

We study the well-posedness of a coupled system of PDEs and ODEs arising in the numerical simulation of electrocardiograms. It consists of a system of degenerate reaction-diffusion equations, the so-called bidomain equations, governing the electrical activity of the heart, and a diffusion equation governing the potential in the surrounding tissues. Global existence of weak solutions is proved f...

The paper proposes a new mathematical FitzHugh—Nagumo model with memory, which describes the propagation of nerve impulse in membrane. consists an integro-differential equation initial conditions (the Cauchy problem). difference kernel (memory function) was chosen as power function so that it can be rewritten terms fractional derivative. For problem, explicit finite-difference scheme is constru...

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...