Non-smooth feedback control for Belousov–Zhabotinskii reaction–diffusion equations: semi-analytical solutions

Abstract

The Belousov–Zhabotinskii reaction is considered in one and two-dimensional reaction–diffusion cells. Feedback control is examined where the feedback mechanism involves varying the concentrations in the boundary reservoir, in response to the concentrations in the centre of the cell. Semi-analytical solutions are developed, via the Galerkin method, which assumes a spatial structure for the solution, and is used to approximate the governing delay partial differential equations by a system of delay ordinary differential equations. The form of feedback control considered, whilst physically realistic, is non-smooth as it has discontinuous derivatives. A stability analysis of the sets of smooth de..