Feedback Stabilization to Nonstationary Solutions of a Class of Reaction Diffusion Equations of FitzHugh-Nagumo Type
نویسندگان
چکیده
Stabilization to a trajectory for the monodomain equations, a coupled nonlinear PDE-ODE system, is investigated. The results rely on stabilization of linear first-order in time nonautonomous evolution equations combined with stabilizability results for the linearized monodomain equations and a fixed point argument to treat local stabilizability of the nonlinear system. Numerical experiments for feedback stabilization of reentry phenomena are included.
منابع مشابه
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...
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 کاملAn 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...
متن کاملStabilization of solutions to a FitzHugh-Nagumo type system
We consider a bistable reaction-diffusion system arising in the theory of phase transitions; it appears in several physical contexts such as thin magnetic films and the microphase separation in diblock copolymer melts. Mathematically it takes the form of an Allen-Cahn equation coupled to an elliptic equation. This system possesses a Lyapunov functional which represents the Gibbs free energy of ...
متن کاملOn the validity of formal asymptotic expansions in Allen-Cahn equation and FitzHugh-Nagumo system with generic initial data
Formal asymptotic expansions have long been used to study the singularly perturbed Allen-Cahn type equations and reaction-diffusion systems, including in particular the FitzHugh-Nagumo system. Despite their successful role, it has been largely unclear whether or not such expansions really represent the actual profile of solutions with rather general initial data. By combining our earlier result...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Control and Optimization
دوره 55 شماره
صفحات -
تاریخ انتشار 2017