منابع مشابه
On the Fitzhugh-Nagumo model
The initial value problem P 0 , in all of the space, for the spatio-temporal FitzHugh-Nagumo equations is analyzed. When the reaction kinetics of the model can be outlined by means of piecewise linear approximations, then the solution of P 0 is explicitly obtained. For periodic initial data are possible damped travelling waves and their speed of propagation is evaluated. The results imply appli...
متن کاملPattern 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...
متن کاملSpatially Discrete FitzHugh--Nagumo Equations
We consider pulse and front solutions to a spatially discrete FitzHugh–Nagumo equation that contains terms to represent both depolarization and hyperpolarization of the nerve axon. We demonstrate a technique for deriving candidate solutions for the McKean nonlinearity and present and apply solvability conditions necessary for existence. Our equation contains both spatially continuous and discre...
متن کاملBifurcations 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...
متن کاملOn a Kinetic Fitzhugh–Nagumo Model of Neuronal Network
We investigate existence and uniqueness of solutions of a McKeanVlasov evolution PDE representing the macroscopic behaviour of interacting Fitzhugh-Nagumo neurons. This equation is hypoelliptic, nonlocal and has unbounded coefficients. We prove existence of a solution to the evolution equation and non trivial stationary solutions. Moreover, we demonstrate uniqueness of the stationary solution i...
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ژورنال
عنوان ژورنال: Scholarpedia
سال: 2006
ISSN: 1941-6016
DOI: 10.4249/scholarpedia.1349