@article{TotzLoeberTotzetal.2018,
  author    = {Totz, Sonja Juliana and L{\"o}ber, Jakob and Totz, Jan Frederik and Engel, Harald},
  title     = {Control of transversal instabilities in reaction-diffusion systems},
  series = {New journal of physics : the open-access journal for physics},
  volume    = {20},
  journal   = {New journal of physics : the open-access journal for physics},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/aabce5},
  pages     = {16},
  year      = {2018},
  abstract  = {In two-dimensional reaction-diffusion systems, local curvature perturbations on traveling waves are typically damped out and vanish. However, if the inhibitor diffuses much faster than the activator, transversal instabilities can arise, leading from flat to folded, spatio-temporally modulated waves and to spreading spiral turbulence. Here, we propose a scheme to induce or inhibit these instabilities via a spatio-temporal feedback loop. In a piecewise-linear version of the FitzHugh-Nagumo model, transversal instabilities and spiral turbulence in the uncontrolled system are shown to be suppressed in the presence of control, thereby stabilizing plane wave propagation. Conversely, in numerical simulations with the modified Oregonator model for the photosensitive Belousov-Zhabotinsky reaction, which does not exhibit transversal instabilities on its own, we demonstrate the feasibility of inducing transversal instabilities and study the emerging wave patterns in a well-controlled manner.},
  language  = {en}
}
@article{PawlikPikovskij2006,
  author    = {Pawlik, Andreas H. and Pikovskij, Arkadij},
  title     = {Control of oscillators coherence by multiple delayed feedback},
  series = {Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics},
  volume    = {358},
  journal   = {Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics},
  number    = {3},
  publisher = {American Institute of Physics},
  address   = {Amsterdam},
  issn      = {0375-9601},
  doi       = {10.1016/j.physleta.2006.05.013},
  pages     = {181 -- 185},
  year      = {2006},
  abstract  = {We demonstrate that a multiple delayed feedback is a powerful tool to control coherence properties of autonomous self-sustained oscillators. We derive the equation for the phase dynamics in presence of noise and delay, and analyze it analytically. In Gaussian approximation a closed set of equations for the frequency and the diffusion constant is obtained. Solutions of these equations are in good agreement with direct numerical simulations.},
  language  = {en}
}