Shaping wave patterns in reaction-diffusion systems.

  title={Shaping wave patterns in reaction-diffusion systems.},
  author={Jakob L{\"o}ber and Steffen Martens and Harald Engel},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  volume={90 6},
We present a method to control the two-dimensional shape of traveling wave solutions to reaction-diffusion systems, such as, interfaces and excitation pulses. Control signals that realize a pregiven wave shape are determined analytically from nonlinear evolution equation for isoconcentration lines as the perturbed nonlinear phase diffusion equation or the perturbed linear eikonal equation. While the control enforces a desired wave shape perpendicular to the local propagation direction, the wave… CONTINUE READING

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