The reaction-diffusion system of Fitzhugh Nagumo is considered. The initialboundary problems with Neumann and Dirichlet conditions are analyzed. By means of an equivalent semilinear integrodifferential equation which characterizes several dissipative models of viscoelasticity, biology, and superconductivity, some results on existence, uniqueness and a priori estimates are deduced both in the li...

Current induced oscillations of a space clamped neuron action potential demonstrates a bifurcation scenario originally encapsulated by the four dimensional Hodgkin-Huxley equations. These oscillations were subsequently described by the two dimensional FitzHugh-Nagumo Equations in close agreement with the HodgkinHuxley theory. It is shown that the FitzHugh-Nagumo equations can to close approxima...

We study the dynamics of a reaction-diffusion system composed of two mutually coupled excitable fibers. We focus on the situation in which dynamical properties of the two fibers are not identical because of the parameter difference between the fibers. Using the spatially one-dimensional FitzHugh-Nagumo equations as a model of a single excitable fiber, we show that the system exhibits a rich var...

Minimal nonlinear dynamic neuron models of the generic bifurcation type may provide the middle way between the detailed models favored by experimentalists and the simplified threshold and rate model of computational neuroscientists. This thesis investigates to which extent generic bifurcation type models grasp the essential dynamical features that may turn out play a role in cooperative neural ...

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.

Abstract We present a computer-assisted approach to prove the existence of Hopf bubbles and degenerate bifurcations in ordinary delay differential equations. apply method rigorously investigate these nonlocal orbit structures FitzHugh–Nagumo equation, extended Lorenz-84 model time-delay SI model.

Oscillating chemical bulk reactions of the Belousov–Zhabotinsky (BZ) type usually show a welldefined periodical color change representing the underlying chemical reactions. Models including up to more than 50 coupled reactions have been developed to describe the BZ-reaction in detail, however, typically a much simpler set of equations is used (i.e. the Brüsselator, the FKN, or the FitzHugh–Nagu...

In the Nenets' own language, "Yamal" means roughly "the end of the earth" or "land's end". It is an apt description for a peninsula that juts well out into the Kara Sea from the mouth of the Ob River, and which serves as the northern endpoint of an annual reindeer (Rangifer tarandus) migration route that, for most animals and modern herders, covers several hundred kilometers. For the reindeer, ...

We investigate a ring of N FitzHugh–Nagumo elements coupled in phase-repulsive fashion and submitted to a (subthreshold) common oscillatory signal and independent Gaussian white noises. This system can be regarded as a reduced version of the one studied in [Phys. Rev. E 64, 041912 (2001)], although externally forced and submitted to noise. The noise-sustained synchronization of the system with ...