TY - JOUR A1 - Feudel, Fred A1 - Feudel, Ulrike T1 - Bifurcations in rotating spherical shell convection under the influence of differential rotation JF - Chaos : an interdisciplinary journal of nonlinear science N2 - 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. Y1 - 2021 U6 - https://doi.org/10.1063/5.0063113 SN - 1054-1500 SN - 1089-7682 VL - 31 IS - 11 PB - AIP CY - Melville ER - TY - JOUR A1 - Gross, Thilo A1 - Feudel, Ulrike T1 - Generalized models as a universal approach to the analysis of nonlinear dynamical systems N2 - 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 Y1 - 2006 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.73.016205 SN - 1539-3755 ER - TY - BOOK A1 - Donner, Reik Volker A1 - Cser, Adrienn A1 - Schwarz, Udo A1 - Otto, Andreas H. A1 - Feudel, Ulrike T1 - An approach to a process model of laser beam melt ablation using methods of linear and non-linear data analysis N2 - 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. Y1 - 2004 SN - 3-527-40430-9 ER - TY - JOUR A1 - Titz, Sven Holger A1 - Kuhlbrodt, Till A1 - Feudel, Ulrike T1 - Grid geometry effects on convection in ocean climate models : a conceptual study N2 - 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 Y1 - 2004 SN - 1463-5003 ER - TY - BOOK A1 - Donner, Reik Volker A1 - Cser, Adrienn A1 - Schwarz, Udo A1 - Otto, Andreas H. A1 - Feudel, Ulrike T1 - An approach to a process model of laser beam melt ablation using methods of linear and non-linear data analysis N2 - 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. Y1 - 2003 SN - 3-928921-88-6 ER - TY - JOUR A1 - Cser, Adrienn A1 - Donner, Reik Volker A1 - Schwarz, Udo A1 - Otto, Andreas H. A1 - Geiger, M. A1 - Feudel, Ulrike T1 - Towards a better understanding of laser beam melt ablation using methods of statistical analysis N2 - 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. Y1 - 2002 SN - 88-87030-44-8 ER - TY - INPR A1 - Feudel, Ulrike T1 - Komplexes Verhalten in multistabilen, schwach dissipativen Systemen N2 - Anhand eines paradigmatischen Modellbeispiels werden die Konsequenzen der Koexistenz vieler Attraktoren auf die globale Dynamik schwach dissipativer Systeme studiert. Es wird gezeigt, dass diese Systeme eine sehr reichhaltige Dynamik besitzen und extrem sensitiv gegenüber Störungen in den Anfangsbedingungen sind. Diese Systeme zeichnen sich durch eine extrem hohe Flexibilität ihres Verhaltens aus. T3 - NLD Preprints - 34 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14412 ER - TY - JOUR A1 - Poon, L. A1 - Grebogi, Celso A1 - Feudel, Ulrike A1 - Yorke, J. A. T1 - Dynamical properties of a simple mechanical system with a large number of coexisting periodic attractors Y1 - 1998 ER - TY - JOUR A1 - Lai, Ying Cheng A1 - Grebogi, Celso A1 - Feudel, Ulrike A1 - Witt, Annette T1 - Basin bifurcation in quasiperiodically forced systems Y1 - 1998 ER - TY - THES A1 - Feudel, Ulrike T1 - Dynamics in between regularity and chaos Y1 - 1996 ER - TY - JOUR A1 - Feudel, Ulrike A1 - Grebogi, Celso T1 - Multistability and the control of complexity Y1 - 1997 SN - 1054-1500 ER - TY - JOUR A1 - Feudel, Ulrike A1 - Grebogi, Celso A1 - Ott, E. T1 - Phase-locking in quasiperiodically forced systems Y1 - 1997 ER - TY - BOOK A1 - Feudel, Ulrike T1 - Komplexes Verhalten in multistabilen, schwach dissipativen Systemen T3 - Preprint NLD Y1 - 1996 VL - 34 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Feudel, Ulrike A1 - Kurths, Jürgen A1 - Neiman, Alexander T1 - The cumulant approach for investigating the noise influence on mode-locking bifurcations T3 - Preprint NLD Y1 - 1995 VL - 16 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Feudel, Ulrike A1 - Jansen, Wolfgang A1 - Kurths, Jürgen A1 - Schwarz, Udo A1 - Voss, Henning U. T1 - Solar variability : simple models and proxy data Y1 - 1997 SN - 4-274-90187-4 ER - TY - JOUR A1 - Bube, Kevin A1 - Neto, Camilo Rodrigues A1 - Donner, Reik Volker A1 - Schwarz, Udo A1 - Feudel, Ulrike T1 - Linear and nonlinear characterization of surfaces from a laser beam melt ablation process N2 - 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 Y1 - 2006 UR - http://iopscience.iop.org/0022-3727/ U6 - https://doi.org/10.1088/0022-3727/39/7/011 SN - 0022-3727 ER - TY - JOUR A1 - Kuhlbrodt, Till A1 - Titz, Sven Holger A1 - Feudel, Ulrike A1 - Rahmstorf, Stefan T1 - A simple model of seasonal open ocean convection. Part II: Labrador Sea stability and stochastic forcing N2 - 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. Y1 - 2001 SN - 1616-7341 ER - TY - JOUR A1 - Cser, Adrienn A1 - Donner, Reik Volker A1 - Schwarz, Udo A1 - Feudel, Ulrike A1 - Otto, Andreas H. T1 - Statistical parameters of a control strategy of laser beam melt ablation N2 - 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. Y1 - 2001 UR - http://www.agnld.uni-potsdam.de/~shw/Paper/2001-EIS.ps ER - TY - JOUR A1 - Kraut, Suso A1 - Feudel, Ulrike A1 - Grebogi, Celso T1 - Preference of attractors in noisy multistable systems Y1 - 1999 ER - TY - INPR A1 - Pikovskij, Arkadij A1 - Zaks, Michael A. A1 - Feudel, Ulrike A1 - Kurths, Jürgen T1 - Singular continuous spectra in dissipative dynamics N2 - 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 Poincaré map have singular power spectra. The other mechanism owes to the logarithmic divergence of the first return times near the saddle point; here the Poincaré 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. T3 - NLD Preprints - 15 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13787 ER - TY - INPR A1 - Pikovskij, Arkadij A1 - Feudel, Ulrike T1 - Characterizing strange nonchaotic attractors N2 - 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. T3 - NLD Preprints - 2 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13405 ER - TY - JOUR A1 - Stark, J. A1 - Feudel, Ulrike A1 - Glendinning, P. A. A1 - Pikovskij, Arkadij T1 - Rotation numbers for quasi-periodically forced monotone circle maps Y1 - 2002 SN - 1468-9367 ER - TY - JOUR A1 - Glendinning, P. A. A1 - Feudel, Ulrike A1 - Pikovskij, Arkadij A1 - Stark, J. T1 - The structure of mode-locking regions in quasi-periodically forced circle maps Y1 - 2000 ER - TY - JOUR A1 - Kuznetsov, Sergey P. A1 - Feudel, Ulrike A1 - Pikovskij, Arkadij T1 - Renormalization group for scaling at the torus-doubling terminal point N2 - 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. Y1 - 1998 ER - TY - JOUR A1 - Pikovskij, Arkadij A1 - Feudel, Ulrike T1 - Comment on "Strange nonchaotic attractors in autonomous and periodically driven systems" N2 - 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. Y1 - 1997 ER - TY - JOUR A1 - Witt, Annette A1 - Feudel, Ulrike A1 - Pikovskij, Arkadij T1 - Birth of strange nonchaotic attractors due to interior crisis Y1 - 1997 ER - TY - JOUR A1 - Kuznetsov, Sergey P. A1 - Pikovskij, Arkadij A1 - Bezrucko, B. P. A1 - Seleznev, E. P. A1 - Feudel, Ulrike T1 - O dinamike nelinejnych sistem po vne¬nim kvaziperiodi§eskim vozdejstviem vblizi to§ki okon§anija linii bifurkatcii udvoenija tora Y1 - 1997 ER -