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

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.

Design of external forces for eliminating traveling wave in a piecewise linear FitzHugh–Nagumo model

“…37 This scheme employs the proper orthogonal decomposition method to obtain a low-dimensional approximation of the system and designs the feedback controller. Although these schemes 37,38 can be generally applied to reaction-diffusion systems and can obtain various types of traveling waves, a certain amount of computation for designing the control signal is required, and the spatially distributed control signal is added over the entire medium. Siehr et al provided a computational approach for targeting characteristic wave properties in reaction-diffusion systems.…”