Exponential Stability for the Schlogl System by Pyragas Feedback

Gugat M, Mateos M, Troeltzsch F (2020)

Publication Type: Journal article

Publication year: 2020

Journal

Vietnam Journal of Mathematics Springer

DOI: 10.1007/s10013-020-00382-7

Abstract

The Schlogl system is governed by a nonlinear reaction-diffusion partial differential equation with a cubic nonlinearity. In this paper, feedback laws of Pyragas-type are presented that stabilize the system in a periodic state with a given period and given boundary traces. We consider the system both with boundary feedback laws of Pyragas type and distributed feedback laws of Pyragas and classical type. Stabilization to periodic orbits is important for medical applications that concern Parkinson's disease. The exponential stability of the closed loop system with respect to the L-2-norm is proved. Numerical examples are provided.

Authors with CRIS profile

Martin Gugat Naturwissenschaftliche Fakultät

Involved external institutions

Universidad de Oviedo ES Spain (ES) Technische Universität Berlin DE Germany (DE)

How to cite

APA:

Gugat, M., Mateos, M., & Troeltzsch, F. (2020). Exponential Stability for the Schlogl System by Pyragas Feedback. Vietnam Journal of Mathematics. https://dx.doi.org/10.1007/s10013-020-00382-7

MLA:

Gugat, Martin, Mariano Mateos, and Fredi Troeltzsch. "Exponential Stability for the Schlogl System by Pyragas Feedback." Vietnam Journal of Mathematics (2020).

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