Targeting characteristic wave properties in reaction-diffusion systems by optimization of external forcing

Jochen Siehr, Mario S. Mommer, Oliver Slaby, and Dirk Lebiedz
Phys. Rev. E 76, 056211 – Published 15 November 2007

Abstract

We consider the targeted manipulation of reaction-diffusion waves by optimization of an external forcing parameter. As an example, we present numerical results for the FitzHugh-Nagumo system exploiting model-based optimization capable of targeting characteristic wave properties such as wavelength, shape, and propagation speed by spatiotemporally controlling electric current. The conceptual basis of our approach is optimal control of periodic orbits in a wave-variable coordinate system. The results are transferred back to the partial differential equation context and validated in numerical simulations. The whole procedure is applicable to any reaction-diffusion model.

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  • Received 16 January 2007

DOI:https://doi.org/10.1103/PhysRevE.76.056211

©2007 American Physical Society

Authors & Affiliations

Jochen Siehr and Mario S. Mommer

  • Interdisciplinary Center for Scientific Computing, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany

Oliver Slaby and Dirk Lebiedz*

  • Center for Biosystem Analysis, Schänzlestraße 1, 79104 Freiburg, Germany

  • *dirk.lebiedz@biologie.uni-freiburg.de

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Issue

Vol. 76, Iss. 5 — November 2007

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