This paper treats the question of robust control of chaos in modified FitzHugh–Nagumo neuron model under external electrical stimulation based on internal model principle. We first present the solution of the global robust output regulation problem for output feedback system with nonlinear exosystem. Then we show that the robust control problem for the modified FitzHugh–Nagumo neuron model can ...

The (constrained) canonical reduction of four-dimensional self-dual Yang–Mills theory to two-dimensional Fitzhugh–Nagumo and the real Newell–Whitehead equations are considered. On the other hand, other methods and transformations are developed to obtain exact solutions for the original two-dimensional Fitzhugh–Nagumo and Newell– Whitehead equations. The corresponding gauge potential Al and the ...

The Exp-function method can be used as an alternative to obtain analytic and approximate solutions of different types of differential equations. In this work Exp -function method is used to find exact solitary wave solutions for Fitzhugh-Nagumo equation. The method is straightforward and concise and its applications for Fitzhugh-Nagumo equation enable one to find exact traveling wave solutions....

We consider a network of reaction diffusion systems of generalized FitzHugh-Nagumo type, where the cubic function is replaced by a polynomial function with odd degree. We deal with asymptotic behaviour and synchronization of the whole network. These results extend a previous work in which we considered particular systems of FitzHugh Nagumo type.

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...

Abstract We will introduce numerical methods for systems of ODEs by considering the celebrated FitzHugh-Nagumo model published FitzHugh [1] in 1961 and, independently, Nagumo et. al. [2] 1962. The is a system ordinary differential equations with two unknowns, and commonly used as simple action potentials excitable pacemaker cells.

Study of neurons plays a key role in the fields of basic and medical research aiming at the development of electrically active implants. The Fitzhugh-Nagumo equations are used to model and simulate the spike generation and propagation in a squid giant axon using Comsol Multiphysics® 3.5a Software. It is shown that the Fitzhugh-Nagumo equations allow for a geometrical explanation of important bi...

In this paper, a FitzHugh-Nagumo model with time delays is investigated. The linear stability of the equilibrium and the existence of Hopf bifurcation with delay τ is investigated. By applying Nyquist criterion, the length of delay is estimated for which stability continues to hold. Numerical simulations for justifying the theoretical results are illustrated. Finally, main conclusions are given...