On the Fitzhugh-Nagumo model

Pattern Formation of the FitzHugh-Nagumo Model: Cellular Automata Approach

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...

An improved pseudospectral approximation of generalized Burger-Huxley and Fitzhugh-Nagumo equations

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...

Robust control of chaos in modified FitzHugh-Nagumo neuron model under external electrical stimulation based on internal model principle

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 ...

Bifurcations for a FitzHugh-Nagumo model with time delays

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...

Qualitative Theory of the FitzHugh-Nagumo Equations

Dynamical Behavior of the linearized Version of the FitzHugh-Nagumo Neural Model

For a linearized version of the FitzHugh–Nagumo model, firing and resetting conditions are defined by analogy with the Integrate and Fire model. The dynamical behavior of the model, subject to periodic synaptic inputs, is investigated both theoretically and numerically, with particular emphasis on the synchronization properties. The study is then extended to a network of two synaptically couple...