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...

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...

Abstract In this work a new mathematical model for complex neural networks is presented by the partly diffusive FitzHugh-Nagumo equations with ensemble boundary coupling. The dissipative dynamics and coupling of solutions are proved sharp uniform estimates. synchronization kind under condition that synaptic stimulation signal strength exceeds threshold quantitatively expressed.

Using the standard van der Pol-FitzHugh-Nagumo excitable medium model, I demonstrate a generic mechanism, diversity, that provokes the emergence of global oscillations from individually quiescent elements in heterogeneous excitable media. This mechanism may be operating in the mammalian pancreas, where excitable beta cells, quiescent when isolated, are found to oscillate when coupled, despite t...

— We study the synchronized/unsynchronized transition as a function of the noise intensity which appears in a system of globally coupled FitzHugh– Nagumo units under the effect of white noise. By the use of the proper definition of an order parameter, we obtain numerically the phase diagram as a function of the noise intensity and coupling constant.

We prove the validity of an averaging principle for a class of systems of slow-fast reactiondiffusion equations with the reaction terms in both equations having polynomial growth, perturbed by a noise of multiplicative type. The models we have in mind are the stochastic Fitzhugh-Nagumo equation arising in neurophysiology and the Ginzburg-Landau equation arising in statistical mechanics.

A mathematical model describing the resistance in cell membrane and nerve fiber is proposed, which is naturally different from that for metal conductors. An allometric scaling law between the resistance and the section area is obtained. In the derivation, He Chengtian's interpolation, which has millennia history, is applied. Most famous models, such as the Hodgkin-Huxley model, FitzHugh-Nagumo ...

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...

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, ...