@article{ArenasBorgeHolthoeferGomezetal.2010,
  author    = {Arenas, Alexandre and Borge-Holthoefer, Javier and Gomez, Sergio and Zamora-Lopez, Gorka},
  title     = {Optimal map of the modular structure of complex networks},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/12/5/053009},
  year      = {2010},
  abstract  = {The modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and the function of complex systems. Generally speaking, modules are islands of highly connected nodes separated by a relatively small number of links. Every module can have the contributions of links from any node in the network. The challenge is to disentangle these contributions to understand how the modular structure is built. The main problem is that the analysis of a certain partition into modules involves, in principle, as much data as the number of modules times the number of nodes. To confront this challenge, here we first define the contribution matrix, the mathematical object containing all the information about the partition of interest, and then we use truncated singular value decomposition to extract the best representation of this matrix in a plane. The analysis of this projection allows us to scrutinize the skeleton of the modular structure, revealing the structure of individual modules and their interrelations.},
  language  = {en}
}
@book{BlechmanLandaRosenblum1995,
  author    = {Blechman, Ilja I. and Landa, Polina S. and Rosenblum, Michael},
  title     = {Synchronization and chaotization in interacting dynamical systems},
  series = {Preprint NLD},
  volume    = {24},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {40 S.},
  year      = {1995},
  language  = {en}
}
@article{BraunDitlevsenKurthsetal.2010,
  author    = {Braun, Holger and Ditlevsen, Peter D. and Kurths, J{\"u}rgen and Mudelsee, Manfred},
  title     = {Limitations of red noise in analysing Dansgaard-Oeschger events},
  issn      = {1814-9324},
  doi       = {10.5194/cp-6-85-2010},
  year      = {2010},
  abstract  = {During the last glacial period, climate records from the North Atlantic region exhibit a pronounced spectral component corresponding to a period of about 1470 years, which has attracted much attention. This spectral peak is closely related to the recurrence pattern of Dansgaard-Oeschger (DO) events. In previous studies a red noise random process, more precisely a first-order autoregressive (AR1) process, was used to evaluate the statistical significance of this peak, with a reported significance of more than 99\%. Here we use a simple mechanistic two-state model of DO events, which itself was derived from a much more sophisticated ocean-atmosphere model of intermediate complexity, to numerically evaluate the spectral properties of random (i.e., solely noise-driven) events. This way we find that the power spectral density of random DO events differs fundamentally from a simple red noise random process. These results question the applicability of linear spectral analysis for estimating the statistical significance of highly non-linear processes such as DO events. More precisely, to enhance our scientific understanding about the trigger of DO events, we must not consider simple "straw men" as, for example, the AR1 random process, but rather test against realistic alternative descriptions.},
  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}
}
@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}
}
@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{BoeckmannBieleNeuberetal.1997,
  author    = {B{\"o}ckmann, Christine and Biele, Jens and Neuber, Roland and Niebsch, Jenny},
  title     = {Retrieval of multimodal aerosol size distribution by inversion of multiwavelength data},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14360},
  year      = {1997},
  abstract  = {The ill-posed problem of aerosol size distribution determination from a small number of backscatter and extinction measurements was solved successfully with a mollifier method which is advantageous since the ill-posed part is performed on exactly given quantities, the points r where n(r) is evaluated may be freely selected. A new twodimensional model for the troposphere is proposed.},
  language  = {en}
}
@unpublished{BoeckmannNiebsch1998,
  author    = {B{\"o}ckmann, Christine and Niebsch, Jenny},
  title     = {Examination of the nonlinear LIDAR-operator : the influence of inhomogeneous absorbing spheres on the operator},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14725},
  year      = {1998},
  abstract  = {The determination of the atmospheric aerosol size distribution is an inverse illposed problem. The shape and the material composition of the air-carried particles are two substantial model parameters. Present evaluation algorithms only used an approximation with spherical homogeneous particles. In this paper we propose a new numerically efficient recursive algorithm for inhomogeneous multilayered coated and absorbing particles. Numerical results of real existing particles show that the influence of the two parameters on the model is very important and therefore cannot be ignored.},
  language  = {en}
}
@book{BoeckmannNiebsch1998,
  author    = {B{\"o}ckmann, Christine and Niebsch, Jenny},
  title     = {Examination of the nonlinear LIDAR-operator : the influence of inhomogeneous absorbing spheres on operator},
  series = {Preprint NLD},
  volume    = {47},
  journal   = {Preprint NLD},
  publisher = {Univ. Potsdam},
  address   = {Potsdam},
  issn      = {1432-2935},
  pages     = {16 S. : Abb.},
  year      = {1998},
  language  = {en}
}