@book{BraunFeudel1996,
  author    = {Braun, Robert and Feudel, Fred},
  title     = {Supertransient chaos in the two-dimensional complex Ginzburg-Landau equation},
  series = {Preprint NLD},
  volume    = {29},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {8 S.},
  year      = {1996},
  language  = {en}
}
@book{BraunFeudelSeehafer1997,
  author    = {Braun, Robert and Feudel, Fred and Seehafer, Norbert},
  title     = {Bifurcations and chaos in an array of forced vortices},
  series = {Preprint NLD},
  volume    = {37},
  journal   = {Preprint NLD},
  publisher = {Univ. Potsdam},
  address   = {Potsdam},
  issn      = {1432-2935},
  pages     = {7 S. : graph. Darst.},
  year      = {1997},
  language  = {en}
}
@article{BraunFeudelSeehafer1997,
  author    = {Braun, Robert and Feudel, Fred and Seehafer, Norbert},
  title     = {Bifurcations and chaos in an array of forced vortices},
  year      = {1997},
  language  = {en}
}
@phdthesis{Braun1997,
  author    = {Braun, Robert},
  title     = {Bifurkationen und Strukturbildung in hydrodynamischen Systemen},
  pages     = {VII, 103 S. : graph. Darst.},
  year      = {1997},
  language  = {de}
}
@book{BraunFeudelGuzdar1998,
  author    = {Braun, Robert and Feudel, Fred and Guzdar, P.},
  title     = {The route to chaos for a two-dimensional externally driven flow : [to appear in Physical Review E]},
  series = {Preprint NLD},
  volume    = {46},
  journal   = {Preprint NLD},
  publisher = {Univ. Potsdam},
  address   = {Potsdam},
  issn      = {1432-2935},
  pages     = {7 S. : graph. Darst.},
  year      = {1998},
  language  = {en}
}
@article{BraunFeudelGuzdar1998,
  author    = {Braun, Robert and Feudel, Fred and Guzdar, P.},
  title     = {The route to chaos for a two-dimensional externally driven flow},
  year      = {1998},
  language  = {en}
}
@article{WittFeudelGebogietal.1998,
  author    = {Witt, Annette and Feudel, Fred and Gebogi, C. and Kurths, J{\"u}rgen and Braun, Robert},
  title     = {Tracer dynamics in a flow of driven vortices},
  series = {Preprint NLD},
  volume    = {51},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1432-2935},
  pages     = {8 S. : graph. Darst.},
  year      = {1998},
  language  = {en}
}
@article{BraunFeudelGebogietal.1999,
  author    = {Braun, Robert and Feudel, Fred and Gebogi, C. and Kurths, J{\"u}rgen and Witt, Annette},
  title     = {Tracer dynamics in a flow of driven vortices},
  year      = {1999},
  language  = {en}
}
@unpublished{BraunFeudelGuzdar1998,
  author    = {Braun, Robert and Feudel, Fred and Guzdar, Parvez},
  title     = {The route to chaos for a two-dimensional externally driven flow},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14717},
  year      = {1998},
  abstract  = {We have numerically studied the bifurcations and transition to chaos in a two-dimensional fluid for varying values of the Reynolds number. These investigations have been motivated by experiments in fluids, where an array of vortices was driven by an electromotive force. In these experiments, successive changes leading to a complex motion of the vortices, due to increased forcing, have been explored [Tabeling, Perrin, and Fauve, J. Fluid Mech. 213, 511 (1990)]. We model this experiment by means of two-dimensional Navier-Stokes equations with a special external forcing, driving a linear chain of eight counter-rotating vortices, imposing stress-free boundary conditions in the vertical direction and periodic boundary conditions in the horizontal direction. As the strength of the forcing or the Reynolds number is raised, the original stationary vortex array becomes unstable and a complex sequence of bifurcations is observed. Several steady states and periodic branches and a period doubling cascade appear on the route to chaos. For increasing values of the Reynolds number, shear flow develops, for which the spatial scale is large compared to the scale of the forcing. Furthermore, we have investigated the influence of the aspect ratio of the container as well as the effect of no-slip boundary conditions at the top and bottom, on the bifurcation scenario.},
  language  = {en}
}
@unpublished{BraunFeudelSeehafer1997,
  author    = {Braun, Robert and Feudel, Fred and Seehafer, Norbert},
  title     = {Bifurcations and chaos in an array of forced vortices},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14564},
  year      = {1997},
  abstract  = {We have studied the bifurcation structure of the incompressible two-dimensional Navier-Stokes equations with a special external forcing driving an array of 8×8 counterrotating vortices. The study has been motivated by recent experiments with thin layers of electrolytes showing, among other things, the formation of large-scale spatial patterns. As the strength of the forcing or the Reynolds number is raised the original stationary vortex array becomes unstable and a complex sequence of bifurcations is observed. The bifurcations lead to several periodic branches, torus and chaotic solutions, and other stationary solutions. Most remarkable is the appearance of solutions characterized by structures on spatial scales large compared to the scale of the forcing. We also characterize the different dynamic regimes by means of tracers injected into the fluid. Stretching rates and Hausdorff dimensions of convected line elements are calculated to quantify the mixing process. It turns out that for time-periodic velocity fields the mixing can be very effective.},
  language  = {en}
}
@unpublished{BraunFeudel1996,
  author    = {Braun, Robert and Feudel, Fred},
  title     = {Supertransient chaos in the two-dimensional complex Ginzburg-Landau equation},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14099},
  year      = {1996},
  abstract  = {We have shown that the two-dimensional complex Ginzburg-Landau equation exhibits supertransient chaos in a certain parameter range. Using numerical methods this behavior is found near the transition line separating frozen spiral solutions from turbulence. Supertransient chaos seems to be a common phenomenon in extended spatiotemporal systems. These supertransients are characterized by an average transient lifetime which depends exponentially on the size of the system and are due to an underlying nonattracting chaotic set.},
  language  = {en}
}