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

Research paper by Jochen J Siehr, Mario S MS Mommer, Oliver O Slaby, Dirk D Lebiedz

Indexed on: 01 Feb '08Published on: 01 Feb '08Published in: Physical review. E, Statistical, nonlinear, and soft matter physics



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.