In this paper, we established traveling wave solutions of the nonlinear evolution equation. The sine-cosine method was used to construct travelling wave solutions of the Fitzhugh-Nagumo equation and Cahn-Allen equation. Graphical interpretation shows that obtained results include periodic and Soliton wave solutions. It is also shown that for α =−1, solutions of Fitzhugh-Nagumo equation coincide...

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...

Small lattices of N nearest-neighbor coupled excitable FitzHugh-Nagumo systems, with time-delayed coupling are studied and compared with systems of FitzHugh-Nagumo oscillators with the same delayed coupling. Bifurcations of equilibria in an N=2 case are studied analytically, and it is then numerically confirmed that the same bifurcations are relevant for the dynamics in the case N>2. Bifurcatio...

A space clamped neural axon along which flows a constant current exhibits current dependent oscillations of the action potential. With increasing current a characteristic Hopf bifurcation scenario can be observed: approximately harmonic small amplitude oscillations arise and bifurcate subsequently into relaxation oscillations of relatively large amplitude. Amplitude and period of the oscillatio...

We analyze a piecewise-linear FitzHugh-Nagumo model. The system exhibits a canard near which both small amplitude and large amplitude periodic orbits exist. The addition of small noise induces mixed-mode oscillations (MMOs) in the vicinity of the canard point. We determine the effect of each model parameter on the stochastically driven MMOs. In particular we show that any parameter variation (s...

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...

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...

The FitzHugh-Nagumo equation has been investigated with a wide array of different methods in the last three decades. Recently a version of the equations with an applied current was analyzed by Champneys, Kirk, Knobloch, Oldeman and Sneyd [5] using numerical continuation methods. They obtained a complicated bifurcation diagram in parameter space featuring a C-shaped curve of homoclinic bifurcati...

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...