Riccati-Based Feedback Control of the Monodomain Equations With the Fitzhugh--Nagumo Model

Riccati-Based Feedback Control of the Monodomain Equations With the Fitzhugh-Nagumo Model

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...

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...

Qualitative Theory of the FitzHugh-Nagumo Equations

FitzHugh-Nagumo equations with generalized diffusive coupling.

The aim of this work is to investigate the dynamics of a neural network, in which neurons, individually described by the FitzHugh-Nagumo model, are coupled by a generalized diffusive term. The formulation we are going to exploit is based on the general framework of graph theory. With the aim of defining the connection structure among the excitable elements, the discrete Laplacian matrix plays a...

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...