@article{FeudelFeudel2021, author = {Feudel, Fred and Feudel, Ulrike}, title = {Bifurcations in rotating spherical shell convection under the influence of differential rotation}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {31}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {11}, publisher = {AIP}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/5.0063113}, pages = {9}, year = {2021}, abstract = {The bifurcations of thermal convection in a rotating spherical shell heated from the inner sphere and driven by the buoyancy of a central gravity field are studied numerically. This model of spherical Rayleigh-Benard convection describes large-scale convection in planets and in the outer zones of celestial bodies. In this work, the influence of an additionally imposed differential rotation of the inner sphere with respect to the outer one on the heat transfer and, more generally, on the whole bifurcation structure is investigated. In addition to numerical simulations, path-following techniques are applied in order to compute both stable and unstable solution branches. The dynamics and the heat transfer are essentially determined by a global bifurcation, which we have identified as a homoclinic bifurcation that consists of a collision of a stable modulated rotating with an unstable rotating wave.}, language = {en} } @article{BubeNetoDonneretal.2006, author = {Bube, Kevin and Neto, Camilo Rodrigues and Donner, Reik Volker and Schwarz, Udo and Feudel, Ulrike}, title = {Linear and nonlinear characterization of surfaces from a laser beam melt ablation process}, issn = {0022-3727}, doi = {10.1088/0022-3727/39/7/011}, year = {2006}, abstract = {We apply linear and nonlinear methods to study the properties of surfaces generated by a laser beam melt ablation process. As a result we present a characterization and ordering of the surfaces depending on the adjusted process parameters. Our findings give some insight into the performance of two widely applied multifractal analysis methods-the detrended fluctuation analysis and the wavelet transform modulus maxima method-on short real world data}, language = {en} } @book{FeudelKurthsNeiman1995, author = {Feudel, Ulrike and Kurths, J{\"u}rgen and Neiman, Alexander}, title = {The cumulant approach for investigating the noise influence on mode-locking bifurcations}, series = {Preprint NLD}, volume = {16}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {20 S.}, year = {1995}, language = {en} } @phdthesis{Feudel1996, author = {Feudel, Ulrike}, title = {Dynamics in between regularity and chaos}, pages = {82 S.}, year = {1996}, language = {en} } @article{FeudelJansenKurthsetal.1997, author = {Feudel, Ulrike and Jansen, Wolfgang and Kurths, J{\"u}rgen and Schwarz, Udo and Voss, Henning U.}, title = {Solar variability : simple models and proxy data}, isbn = {4-274-90187-4}, year = {1997}, language = {en} } @article{WittFeudelPikovskij1997, author = {Witt, Annette and Feudel, Ulrike and Pikovskij, Arkadij}, title = {Birth of strange nonchaotic attractors due to interior crisis}, year = {1997}, language = {en} } @article{FeudelGrebogiOtt1997, author = {Feudel, Ulrike and Grebogi, Celso and Ott, E.}, title = {Phase-locking in quasiperiodically forced systems}, year = {1997}, language = {en} } @article{FeudelGrebogi1997, author = {Feudel, Ulrike and Grebogi, Celso}, title = {Multistability and the control of complexity}, issn = {1054-1500}, year = {1997}, language = {en} } @misc{PikovskijFeudel1997, author = {Pikovskij, Arkadij and Feudel, Ulrike}, title = {Comment on "Strange nonchaotic attractors in autonomous and periodically driven systems"}, year = {1997}, abstract = {The problem of the existence of strange nonchaotic attractors (SNA's) in autonomous systems is discussed. It is demonstrated that the recently reported example of a SNA in an autonomous system [V. S. Anishchenko et al., Phys. Rev. E 54, 3231 (1996)] is in fact a chaotic attractor with positive largest Lyapunov exponent.}, language = {en} } @article{LaiGrebogiFeudeletal.1998, author = {Lai, Ying Cheng and Grebogi, Celso and Feudel, Ulrike and Witt, Annette}, title = {Basin bifurcation in quasiperiodically forced systems}, year = {1998}, language = {en} } @article{PoonGrebogiFeudeletal.1998, author = {Poon, L. and Grebogi, Celso and Feudel, Ulrike and Yorke, J. A.}, title = {Dynamical properties of a simple mechanical system with a large number of coexisting periodic attractors}, year = {1998}, language = {en} } @article{KuznetsovFeudelPikovskij1998, author = {Kuznetsov, Sergey P. and Feudel, Ulrike and Pikovskij, Arkadij}, title = {Renormalization group for scaling at the torus-doubling terminal point}, year = {1998}, abstract = {The quasiperiodically forced logistic map is analyzed at the terminal point of the torus-doubling bifurcation curve, where the dynamical regimes of torus, doubled torus, strange nonchaotic attractor, and chaos meet. Using the renormalization group approach we reveal scaling properties both for the critical attractor and for the parameter plane topography near the critical point.}, language = {en} } @article{KrautFeudelGrebogi1999, author = {Kraut, Suso and Feudel, Ulrike and Grebogi, Celso}, title = {Preference of attractors in noisy multistable systems}, year = {1999}, language = {en} } @article{GlendinningFeudelPikovskijetal.2000, author = {Glendinning, P. A. and Feudel, Ulrike and Pikovskij, Arkadij and Stark, J.}, title = {The structure of mode-locking regions in quasi-periodically forced circle maps}, year = {2000}, language = {en} } @article{CserDonnerSchwarzetal.2001, author = {Cser, Adrienn and Donner, Reik Volker and Schwarz, Udo and Feudel, Ulrike and Otto, Andreas H.}, title = {Statistical parameters of a control strategy of laser beam melt ablation}, year = {2001}, abstract = {Laser beam melt ablation - a contact-free machining process - offers several advantages compared to conventional processing mechanisms: there exists no tool wear and even extremely hard or brittle materials can be processed. During ablation the workpiece is molten by a CO2-laser beam, this melt is then driven out by the impulse of a process gas. The idea behind laser ablation is rather simple, but it has a major limitation in practical applications: with increasing ablation rates surface quality of the workpiece processed declines rapidly. At high ablation rates, depending on the process parameters different periodic-like structures can be observed on the ablated surface. These structures show a dependence on the line energy, which has been identified as a fundamental control parameter. In dependence on this parameter several regimes with different behaviours of the process have been separated. These regimes are distinguishable as well in the surfaces obtained as in the signals gained by the measurement of the process emissions. Further aim is to identify the different modes of the system and reach a deeper understanding of the dynamics of the molten material in order to understand the formation of these surface structures. With this it should be possible to influence the system in the direction of avoiding structure formation even at high ablation rates. Relying on the results on-line monitoring and control of the process should be studied.}, language = {en} } @article{KuhlbrodtTitzFeudeletal.2001, author = {Kuhlbrodt, Till and Titz, Sven Holger and Feudel, Ulrike and Rahmstorf, Stefan}, title = {A simple model of seasonal open ocean convection. Part II: Labrador Sea stability and stochastic forcing}, issn = {1616-7341}, year = {2001}, abstract = {Aspects of open ocean deep convection variability are explored with a two-box model. In order to place the model in a region of parameter space relevant to the real ocean, it is fitted to observational data from the Labrador Sea. A systematic fit to OWS Bravo data allows us to determine the model parameters and to locate the position of the Labrador Sea on a stability diagram. The model suggests that the Labrador Sea is in a bistable regime where winter convection can be either ?on? or ?off?, with both these possibilities being stable climate states. When shifting the surface buoyancy forcing slightly to warmer or fresher conditions, the only steady solution is one without winter convection. We then introduce short-term variability by adding a noise term to the surface temperature forcing, turning the box model into a stochastic climate model. The surface forcing anomalies generated in this way induce jumps between the two model states. These state transitions occur on the interannual to decadal timescale. Changing the average surface forcing towards more buoyant conditions lowers the frequency of convection. However, convection becomes more frequent with stronger variability in the surface forcing. As part of the natural variability, there is a non-negligible probability for decadal interruptions of convection. The results highlight the role of surface forcing variability for the persistence of convection in the ocean.}, language = {en} } @article{StarkFeudelGlendinningetal.2002, author = {Stark, J. and Feudel, Ulrike and Glendinning, P. A. and Pikovskij, Arkadij}, title = {Rotation numbers for quasi-periodically forced monotone circle maps}, issn = {1468-9367}, year = {2002}, language = {en} } @article{CserDonnerSchwarzetal.2002, author = {Cser, Adrienn and Donner, Reik Volker and Schwarz, Udo and Otto, Andreas H. and Geiger, M. and Feudel, Ulrike}, title = {Towards a better understanding of laser beam melt ablation using methods of statistical analysis}, isbn = {88-87030-44-8}, year = {2002}, abstract = {Laser beam melt ablation, as a contact free machining process, offers several advantages compared to conventional processing mechanisms. Although the idea behind it is rather simple, the process has a major limitation: with increasing ablation rate surface quality of the workpiece processed declines rapidly. The structures observed show a clear dependence of the line energy. In dependence of this parameter several regimes of the process have been separated. These are clearly distinguishable as well in the surfaces obtained as in the signals gained by the measurement of the process emissions which is the observed quantity chosen.}, language = {en} } @book{DonnerCserSchwarzetal.2003, author = {Donner, Reik Volker and Cser, Adrienn and Schwarz, Udo and Otto, Andreas H. and Feudel, Ulrike}, title = {An approach to a process model of laser beam melt ablation using methods of linear and non-linear data analysis}, isbn = {3-928921-88-6}, year = {2003}, abstract = {As a non-contact process laser beam melt ablation offers several advantages compared to conventional processing mechanisms. During ablation the surface of the workpiece is molten by the energy of a CO2-laser beam, this melt is then driven out by the impulse of an additional process gas. Although the idea behind laser beam melt ablation is rather simple, the process itself has a major limitation in practical applications: with increasing ablation rate surface quality of the workpiece processed declines rapidly. With different ablation rates different surface structures can be distinguished, which can be characterised by suitable surface parameters. The corresponding regimes of pattern formation are found in linear and non-linear statistical properties of the recorded process emissions as well. While the ablation rate can be represented in terms of the line-energy, this parameter does not provide sufficient information about the full behaviour of the system. The dynamics of the system is dominated by oscillations due to the laser cycle but includes some periodically driven non-linear processes as well. Upon the basis of the measured time series, a corresponding model is developed. The deeper understanding of the process can be used to develop strategies for a process control.}, language = {en} } @article{TitzKuhlbrodtFeudel2004, author = {Titz, Sven Holger and Kuhlbrodt, Till and Feudel, Ulrike}, title = {Grid geometry effects on convection in ocean climate models : a conceptual study}, issn = {1463-5003}, year = {2004}, abstract = {Ocean convection is a highly non-linear and local process. Typically, a small-scale phenomenon of this kind entails numerical problems in the modelling of ocean circulation. One of the tasks to solve is the improvement of convection parameterization schemes, but the question of grid geometry also plays a considerable role. Here, this question is studied in the context of global ocean models coupled to an atmosphere model. Such ocean climate models have mostly structured, coarsely resolved grids. Using a simple conceptual two-layer model, we compare the discretization effects of a rectangular grid with those of a grid with hexagonal grid cells, focussing on average properties of the ocean. It turns out that systematic errors tend to be clearly smaller with the hexagonal grid. In a hysteresis experiment with the atmospheric boundary condition as a hysteresis parameter, the spatially averaged behaviour shows nonnegligible artificial steps for quadratic grid cells. This bias is reduced with the hexagonal grid. The same holds for the directional sensitivity (or horizontal anisotropy) which is found for different angles of the advection velocity. The grid with hexagonal grid cells shows much more isotropic results. From the limited viewpoint of these test experiments, it seems that the hexagonal grid (i.e. icosahedral-hexagonal grids on the sphere) is recommendable for ocean climate models. (C) 2003 Elsevier Ltd. All rights reserved}, language = {en} } @book{DonnerCserSchwarzetal.2004, author = {Donner, Reik Volker and Cser, Adrienn and Schwarz, Udo and Otto, Andreas H. and Feudel, Ulrike}, title = {An approach to a process model of laser beam melt ablation using methods of linear and non-linear data analysis}, isbn = {3-527-40430-9}, year = {2004}, abstract = {As a non-contact process laser beam melt ablation offers several advantages compared to conventional processing mechanisms. During ablation the surface of the workpiece is molten by the energy of a CO2-laser beam, this melt is then driven out by the impulse of an additional process gas. Although the idea behind laser beam melt ablation is rather simple, the process itself has a major limitation in practical applications: with increasing ablation rate surface quality of the workpiece processed declines rapidly. With different ablation rates different surface structures can be distinguished, which can be characterised by suitable surface parameters. The corresponding regimes of pattern formation are found in linear and non-linear statistical properties of the recorded process emissions as well. While the ablation rate can be represented in terms of the line-energy, this parameter does not provide sufficient information about the full behaviour of the system. The dynamics of the system is dominated by oscillations due to the laser cycle but includes some periodically driven non-linear processes as well. Upon the basis of the measured time series, a corresponding model is developed. The deeper understanding of the process can be used to develop strategies for a process control.}, language = {en} } @article{GrossFeudel2006, author = {Gross, Thilo and Feudel, Ulrike}, title = {Generalized models as a universal approach to the analysis of nonlinear dynamical systems}, issn = {1539-3755}, doi = {10.1103/Physreve.73.016205}, year = {2006}, abstract = {We present a universal approach to the investigation of the dynamics in generalized models. In these models the processes that are taken into account are not restricted to specific functional forms. Therefore a single generalized models can describe a class of systems which share a similar structure. Despite this generality, the proposed approach allows us to study the dynamical properties of generalized models efficiently in the framework of local bifurcation theory. The approach is based on a normalization procedure that is used to identify natural parameters of the system. The Jacobian in a steady state is then derived as a function of these parameters. The analytical computation of local bifurcations using computer algebra reveals conditions for the local asymptotic stability of steady states and provides certain insights on the global dynamics of the system. The proposed approach yields a close connection between modelling and nonlinear dynamics. We illustrate the investigation of generalized models by considering examples from three different disciplines of science: a socioeconomic model of dynastic cycles in china, a model for a coupled laser system and a general ecological food web}, language = {en} } @unpublished{PikovskijZaksFeudeletal.1995, author = {Pikovskij, Arkadij and Zaks, Michael A. and Feudel, Ulrike and Kurths, J{\"u}rgen}, title = {Singular continuous spectra in dissipative dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13787}, year = {1995}, abstract = {We demonstrate the occurrence of regimes with singular continuous (fractal) Fourier spectra in autonomous dissipative dynamical systems. The particular example in an ODE system at the accumulation points of bifurcation sequences associated to the creation of complicated homoclinic orbits. Two different machanisms responsible for the appearance of such spectra are proposed. In the first case when the geometry of the attractor is symbolically represented by the Thue-Morse sequence, both the continuous-time process and its descrete Poincar{\´e} map have singular power spectra. The other mechanism owes to the logarithmic divergence of the first return times near the saddle point; here the Poincar{\´e} map possesses the discrete spectrum, while the continuous-time process displays the singular one. A method is presented for computing the multifractal characteristics of the singular continuous spectra with the help of the usual Fourier analysis technique.}, 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} }