@unpublished{Jansen1996,
  author    = {Jansen, Wolfgang},
  title     = {A note on the determination of the type of communication areas},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14339},
  year      = {1996},
  abstract  = {The paper presents a method that determines, by standard numerical means, the type of mutual relations of fold and flip bifurcations (configured as a so-called communication area) of a map. Equation systems are developed for the computation of points where a transition between areas of different types occurs. Furthermore, it is shown that saddle area<->spring area transitions can exist which have not yet been considered in the literature. Analytical conditions of that transition are derived.},
  language  = {en}
}
@unpublished{SeehaferZienickeFeudel1996,
  author    = {Seehafer, Norbert and Zienicke, Egbert and Feudel, Fred},
  title     = {Absence of magnetohydrodynamic activity in the voltage-driven sheet pinch},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14328},
  year      = {1996},
  abstract  = {We have numerically studied the bifurcation properties of a sheet pinch with impenetrable stress-free boundaries. An incompressible, electrically conducting fluid with spatially and temporally uniform kinematic viscosity and magnetic diffusivity is confined between planes at x1=0 and 1. Periodic boundary conditions are assumed in the x2 and x3 directions and the magnetofluid is driven by an electric field in the x3 direction, prescribed on the boundary planes. There is a stationary basic state with the fluid at rest and a uniform current J=(0,0,J3). Surprisingly, this basic state proves to be stable and apparently to be the only time-asymptotic state, no matter how strong the applied electric field and irrespective of the other control parameters of the system, namely, the magnetic Prandtl number, the spatial periods L2 and L3 in the x2 and x3 directions, and the mean values B¯2 and B¯3 of the magnetic-field components in these directions.},
  language  = {en}
}
@unpublished{MaassPereverzevRamlauetal.1998,
  author    = {Maaß, Peter and Pereverzev, Sergei V. and Ramlau, Ronny and Solodky, Sergei G.},
  title     = {An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14739},
  year      = {1998},
  abstract  = {The aim of this paper is to describe an efficient strategy for descritizing ill-posed linear operator equations of the first kind: we consider Tikhonov-Phillips-regularization χ^δ α = (a * a + α I)^-1 A * y ^δ with a finite dimensional approximation A n instead of A. We propose a sparse matrix structure which still leads to optimal convergences rates but requires substantially less scalar products for computing A n compared with standard methods.},
  language  = {en}
}
@unpublished{SchumacherSeehafer1999,
  author    = {Schumacher, J{\"o}rg and Seehafer, Norbert},
  title     = {Bifurcation analysis of the plane sheet pinch},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14926},
  year      = {1999},
  abstract  = {A numerical bifurcation analysis of the electrically driven plane sheet pinch is presented. The electrical conductivity varies across the sheet such as to allow instability of the quiescent basic state at some critical Hartmann number. The most unstable perturbation is the two-dimensional tearing mode. Restricting the whole problem to two spatial dimensions, this mode is followed up to a time-asymptotic steady state, which proves to be sensitive to three-dimensional perturbations even close to the point where the primary instability sets in. A comprehensive three-dimensional stability analysis of the two-dimensional steady tearing-mode state is performed by varying parameters of the sheet pinch. The instability with respect to three-dimensional perturbations is suppressed by a sufficiently strong magnetic field in the invariant direction of the equilibrium. For a special choice of the system parameters, the unstably perturbed state is followed up in its nonlinear evolution and is found to approach a three-dimensional steady state.},
  language  = {en}
}
@unpublished{FeudelSeehaferSchmidtmann1995,
  author    = {Feudel, Fred and Seehafer, Norbert and Schmidtmann, Olaf},
  title     = {Bifurcation phenomena of the magnetofluid equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13585},
  year      = {1995},
  abstract  = {We report on bifurcation studies for the incompressible magnetohydrodynamic equations in three space dimensions with periodic boundary conditions and a temporally constant external forcing. Fourier reprsentations of velocity, pressure and magnetic field have been used to transform the original partial differential equations into systems of ordinary differential equations (ODE), to which then special numerical methods for the qualitative analysis of systems of ODE have been applied, supplemented by the simulative calculation of solutions for selected initial conditions. In a part of the calculations, in order to reduce the number of modes to be retained, the concept of approximate inertial manifolds has been applied. For varying (incereasing from zero) strength of the imposed forcing, or varying Reynolds number, respectively, time-asymptotic states, notably stable stationary solutions, have been traced. A primary non-magnetic steady state loses, in a Hopf bifurcation, stability to a periodic state with a non-vanishing magnetic field, showing the appearance of a generic dynamo effect. From now on the magnetic field is present for all values of the forcing. The Hopf bifurcation is followed by furhter, symmetry-breaking, bifurcations, leading finally to chaos. We pay particular attention to kinetic and magnetic helicities. The dynamo effect is observed only if the forcing is chosen such that a mean kinetic helicity is generated; otherwise the magnetic field diffuses away, and the time-asymptotic states are non-magnetic, in accordance with traditional kinematic dynamo theory.},
  language  = {en}
}
@unpublished{ScheelSeehafer1997,
  author    = {Scheel, Stefan and Seehafer, Norbert},
  title     = {Bifurcation to oscillations in three-dimensional Rayleigh-B{\´e}nard convection},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14370},
  year      = {1997},
  abstract  = {Three-dimensional bouyancy-driven convection in a horizontal fluid layer with stress-free boundary conditions at the top and bottom and periodic boundary conditions in the horizontal directions is investigated by means of numerical simulation and bifurcation-analysis techniques. The aspect ratio is fixed to a value of 2√2 and the Prandtl number to a value of 6.8. Two-dimensional convection rolls are found to be stable up to a Rayleigh number of 17 950, where a Hopf bifurcation leads to traveling waves. These are stable up to a Rayleigh number of 30 000, where a secondary Hopf bifurcation generates modulated traveling waves. We pay particular attention to the symmetries of the solutions and symmetry breaking by the bifurcations.},
  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{FeudelSeehafer1995,
  author    = {Feudel, Fred and Seehafer, Norbert},
  title     = {Bifurcations and pattern formation in a 2D Navier-Stokes fluid},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13907},
  year      = {1995},
  abstract  = {We report on bifurcation studies for the incompressible Navier-Stokes equations in two space dimensions with periodic boundary conditions and an external forcing of the Kolmogorov type. Fourier representations of velocity and pressure have been used to approximate the original partial differential equations by a finite-dimensional system of ordinary differential equations, which then has been studied by means of bifurcation-analysis techniques. A special route into chaos observed for increasing Reynolds number or strength of the imposed forcing is described. It includes several steady states, traveling waves, modulated traveling waves, periodic and torus solutions, as well as a period-doubling cascade for a torus solution. Lyapunov exponents and Kaplan-Yorke dimensions have been calculated to characterize the chaotic branch. While studying the dynamics of the system in Fourier space, we also have transformed solutions to real space and examined the relation between the different bifurcations in Fourier space and toplogical changes of the streamline portrait. In particular, the time-dependent solutions, such as, e.g., traveling waves, torus, and chaotic solutions, have been characterized by the associated fluid-particle motion (Lagrangian dynamics).},
  language  = {en}
}
@unpublished{Jansen1995,
  author    = {Jansen, Wolfgang},
  title     = {CANDYS/QA : algorithms, programs, and user's manual},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13920},
  year      = {1995},
  abstract  = {Contents: I. Algorithms 1. Theoretical Backround 2. Numerical Procedures 3. Graph Representation of the Solutions 4. Applications and Example II. Users' Manual 5. About the Program 6. The Course of a Qualitative Analysis 7. The Model Module 8. Input description 9. Output Description 10. Example 11. Graphics},
  language  = {en}
}
@unpublished{PikovskijFeudel1994,
  author    = {Pikovskij, Arkadij and Feudel, Ulrike},
  title     = {Characterizing strange nonchaotic attractors},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13405},
  year      = {1994},
  abstract  = {Strange nonchaotic attractors typically appear in quasiperiodically driven nonlinear systems. Two methods of their characterization are proposed. The first one is based on the bifurcation analysis of the systems, resulting from periodic approximations of the quasiperiodic forcing. Secondly, we propose th characterize their strangeness by calculating a phase sensitivity exponent, that measures the sensitivity with respect to changes of the phase of the external force. It is shown, that phase sensitivity appears if there is a non-zero probability for positive local Lyapunov exponents to occur.},
  language  = {en}
}