Controlling pulse stability in singularly perturbed reaction-diffusion systems

2023/04/06 by Veerman, Frits, Schneider, Isabelle
#Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2304.03342

Abstract

The aim of this paper is to investigate the use of Pyragas control on the stability of stationary, localised coherent structures in a general class of two-component, singularly perturbed, reaction-diffusion systems. We use noninvasive Pyragas-like proportional feedback control to stabilise a singular pulse solution to a two-component, singularly perturbed reaction-diffusion system. We show that in a significant region of parameter space, the control can be adjusted to stabilise an otherwise unstable pulse.

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