Bifurcating Solutions to the Monodomain Model Equipped with FitzHugh-Nagumo Kinetics
نویسندگان
چکیده
منابع مشابه
Bifurcating Solutions to the Monodomain Model Equipped with FitzHugh-Nagumo Kinetics
We study Hopf bifurcation solutions to the Monodomain model equipped with FitzHughNagumo cell dynamics. This reaction-diffusion system plays an important role in the field of electrocardiology as a tractable mathematical model of the electrical activity in the human heart. In our setting the bounded spatial domain consists of two subdomains: a collection of automatic cells surrounded by collect...
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Feedback control for the monodomain equations is studied. The dynamics of interest are governed by a coupled PDE-ODE reaction diffusion system with non-monotone nonlinearity of FitzHugh-Nagumo type. A localized distributed control is used to locally stabilize the nonlinear system. This is achieved by a Riccati-based feedback law, determined by the linearized system. It is shown that the Riccati...
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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...
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During present investigation, a direct algebraic method based on complex solutions of nonlinear partial differential equations is developed and tested in the case of generalised Burgers–Huxley equation. The proposed scheme can be used in a wide class of nonlinear reaction–diffusion equations. These calculations demonstrate that the accuracy of the direct algebraic solutions is quite high even i...
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...
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ژورنال
عنوان ژورنال: Journal of Applied Mathematics
سال: 2009
ISSN: 1110-757X,1687-0042
DOI: 10.1155/2009/292183