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...

We explore an embryonic heart model that couples electrophysiology and muscle-force generation to flow induced using a 2D fluid-structure interaction framework based on the immersed boundary method. The propagation of action potentials are coupled to muscular contraction and hence the overall pumping dynamics. In comparison to previous models, the electro-dynamical model does not use prescribed...

We derive and study two-dimensional generalizations of integrate-and-fire models which can be found from a piecewise linear idealization of the FitzHugh-Nagumo or Morris-Lecar model. These models give rise to new properties not present in one-dimensional integrate-and-fire models. A detailed analytical study of the models is presented. In particular, (i) for the piecewise linear FitzHugh-Nagumo...

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, ...

In this paper, we develop an accurate and ef£cient Haar wavelet method for well-known FitzHugh-Nagumo equation. The proposed scheme can be used to a wide class of nonlinear reaction-diffusion equations. The power of this manageable method is con£rmed. Moreover the use of Haar wavelets is found to be accurate, simple, fast, ¤exible, convenient, small computation costs and computationally attract...

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 ...

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.

This paper investigates travelling wave solutions of the FitzHugh-Nagumo equation from the viewpoint of fast-slow dynamical systems. These solutions are homoclinic orbits of a three dimensional vector field depending upon system parameters of the FitzHugh-Nagumo model and the wave speed. Champneys et al. [A.R. Champneys, V. Kirk, E. Knobloch, B.E. Oldeman, and J. Sneyd, When Shilnikov meets Hop...