Backstepping stabilization of the Fitzhugh-Nagumo system arising in nonlinear spatial-temporal evolutionary processes

This paper deals with the boundary stabilization problem for the FitzHugh-Nagumo system, which is a coupled system of a non-linear diffusion partial differential equation (PDE) and an ordinary differential equation (ODE). Using the backstepping transformation and a boundary feedback controller, the original unstable system can be converted into a nonlinear target system, from which the stability analysis is obtained when the initial data are small enough. The effectiveness of the proposed feedback controller is illustrated by a numerical simulation.

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