Fitzhugh-Nagumo denklemlerinin kararlılık analizi

FitzHugh-Nagumo system is generally used to model some biological phenomena and electrical circuits. This system is obtained by a reduction of the Hodgkin-Huxley system which is also widely used but harder to analyze. In this work, our aim is to study the existence and uniqueness of solutions to reaction-diffusion equations and some stability properties of FitzHugh-Nagumo equations. We firstly consider the problem of local and global existence and uniqueness of the solution to the reaction-diffusion equation. Then, we study the problem of stabilization of solutions of FitzHugh-Nagumo system on a bounded domain. We show that by applying a feedback controller on a subdomain, the system can be stabilized via this feedback controller. Finally, considering again a FitzHugh-Nagumo system, we study the continuous dependence of solutions to this system on the diffusivity coefficient.