@article{FeudelSeehaferRuediger1996, author = {Feudel, Fred and Seehafer, Norbert and R{\"u}diger, Sten}, title = {Symmetry breaking bifurcations for the magnetohydrodynamic equations with helical forcing}, series = {Preprint NLD}, volume = {31}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {10 S.}, year = {1996}, language = {en} } @book{SeehaferZienickeFeudel1996, author = {Seehafer, Norbert and Zienicke, Egbert and Feudel, Fred}, title = {Absence of magnetohydrodynamic activity in the voltage-driven sheet}, series = {Preprint NLD}, volume = {32}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {8 S.}, year = {1996}, language = {en} } @book{Morin1995, author = {Morin, Paul}, title = {Visualization in the geosciences : course notes}, series = {Preprint NLD}, volume = {19}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {123 S.}, year = {1995}, language = {en} } @book{Jansen1995, author = {Jansen, Wolfgang}, title = {CANDYS/QA : algorithms, programs and user's manual}, series = {Preprint NLD}, volume = {27}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {140 S.}, year = {1995}, 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} } @book{Meister1994, author = {Meister, Claudia-Veronika}, title = {Stochastic forces on electrons in the solar flare plasma}, series = {Preprint NLD}, volume = {7}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {12 S.}, year = {1994}, language = {en} } @article{MeisterLiperovskySchlegeletal.1995, author = {Meister, Claudia-Veronika and Liperovsky, Viktor A. and Schlegel, K. and Haldoupis, Ch.}, title = {Currents and turbulence in and near mid-latitude sporadic e-layers caused by strong acoustic impulses}, series = {Preprint NLD}, volume = {11}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {15 S.}, year = {1995}, language = {en} } @article{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}, series = {Preprint NLD}, volume = {48}, journal = {Preprint NLD}, publisher = {Univ. Potsdam}, address = {Potsdam}, issn = {1432-2935}, pages = {19 S.}, year = {1998}, 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} } @article{LiperovskyPochotelovLiperovskayaetal.1998, author = {Liperovsky, Viktor A. and Pochotelov, O. A. and Liperovskaya, E. V. and Parrot, M. and Meister, Claudia-Veronika and Alimov, O. A.}, title = {Modifications of sporadic E-layers caused by seismic activity}, series = {Preprint NLD}, volume = {49}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, issn = {1432-2935}, pages = {46 S. : graph. Darst.}, year = {1998}, language = {en} } @book{Dicken1998, author = {Dicken, Volker}, title = {Simultaneous activity and attenuation reconstruction in emission tomography}, series = {Preprint NLD}, volume = {50}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, issn = {1432-2935}, pages = {27 S. : graph. Darst.}, year = {1998}, language = {en} } @book{VolosevichMeister1998, author = {Volosevich, A. V. and Meister, Claudia-Veronika}, title = {Nonlinear interaction of Farley-Buneman waves}, series = {Preprint NLD}, volume = {52}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, issn = {1432-2935}, pages = {13 S.}, year = {1998}, language = {en} } @book{Jansen1996, author = {Jansen, Wolfgang}, title = {A note on the determination of the type of communication areas}, series = {Preprint NLD}, volume = {33}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {32 S.}, year = {1996}, 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} } @book{MaassRieder1996, author = {Maaß, Peter and Rieder, Andreas}, title = {Wavelet-accelerated Tikhonov-Phillips regularization with applications}, series = {Preprint NLD}, volume = {30}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {25 S.}, year = {1996}, language = {en} } @book{VossKurthsSchwarz1996, author = {Voss, Henning U. and Kurths, J{\"u}rgen and Schwarz, Udo}, title = {Reconstruction of grand minima of solar activity from radiocarbon data : linear and nonlinear signal analysis}, series = {Preprint NLD}, volume = {28}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {14 S.}, year = {1996}, language = {en} } @book{Montada1996, author = {Montada, Leo}, title = {Gerechtigkeitsanspr{\"u}che und Ungerechtigkeitserleben in den neuen Bundesl{\"a}ndern}, series = {Bericht / Zentrum f{\"u}r Gerechtigkeitsforschung, Potsdam}, volume = {4}, journal = {Bericht / Zentrum f{\"u}r Gerechtigkeitsforschung, Potsdam}, publisher = {Univ.}, address = {Potsdam}, pages = {55 S.}, year = {1996}, language = {de} } @book{Feudel1996, author = {Feudel, Ulrike}, title = {Komplexes Verhalten in multistabilen, schwach dissipativen Systemen}, series = {Preprint NLD}, volume = {34}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {11 S.}, year = {1996}, language = {de} } @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} } @book{LiperovskijMeister1995, author = {Liperovskij, Viktor A. and Meister, Claudia-Veronika}, title = {Sporadic e-layers as current generator : two-dimensional model}, series = {Preprint NLD}, volume = {20}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {23 S.}, year = {1995}, language = {en} } @book{MeisterKubyshkin1995, author = {Meister, Claudia-Veronika and Kubyshkin, I. V.}, title = {Recalculation of the diffusion tensor for plasmas with ion-acoustic turbulence}, series = {Preprint NLD}, volume = {26}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {16 S.}, year = {1995}, language = {en} } @book{Meister1995, author = {Meister, Claudia-Veronika}, title = {Stochastic forces in space plasmas with ion-acoustic and lower-hybrid-drift turbulence}, series = {Preprint NLD}, volume = {10}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {23 S.}, year = {1995}, language = {en} } @book{RosenblumKurths1995, author = {Rosenblum, Michael and Kurths, J{\"u}rgen}, title = {A model of neural control of heart rate}, series = {Preprint NLD}, volume = {12}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {22 S.}, year = {1995}, language = {en} } @book{SpahnHertzschBrilliantov1995, author = {Spahn, Frank and Hertzsch, Jan-Martin and Brilliantov, Nikolai V.}, title = {The role of particle collisions for the dynamics in planetary rings}, series = {Preprint NLD}, volume = {14}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {23 S.}, year = {1995}, language = {en} } @article{Schwarz1994, author = {Schwarz, Udo}, title = {Das Maunder-Minimum : alles sonnenklar, oder?}, year = {1994}, abstract = {Im vorletzten Absatz des o.g. Kurzberichtes befindet sich eine falsche Aussage zur C14-Produktion waehrend des Maunder-Minimums. Wie aus der in meiner Abbildung gezeigten Delta C14-Haeufigkeit fuer den Zeitraum des Maunder-Minimums hervorgeht, war die C14-Produktion zu dieser Zeit erhoeht statt, wie von Herrn Buehrke und anderen Autoren in der Literatur behauptet, erniedrigt. Die allgemein akzeptierte Begruendung fuer die erhoehte C14-Produktion lautet: Der geringere Sonnenwind schirmt die Erde weniger stark von der kosmischen Strahlung ab.}, language = {de} } @article{KurthsSchwarzParlitzetal.1994, author = {Kurths, J{\"u}rgen and Schwarz, Udo and Parlitz, Ulrich and Sonett, Charles P.}, title = {Testing for nonlinearity in radiocarbon data}, issn = {1023-5809}, year = {1994}, abstract = {The radiocarbon record that has been extended from 7199 BC to 1891 AD is of fundamental importance to understand century-scale variations of solar activity. We have, therefore, studied how to extract information from dynamic reconstructions of this observational record. Using some rather unusual methods of nonlinear dynamics, we have found that the data are significantly different from linear colored noise and that there is some evidence of nonlinear behavior. The method of recurrence plots exhibits that the grand minima of solar activity are quite different in their recurrence. Most remarkably, it suggests that the recent epoch seems to be similar to the Medieval maximum.}, language = {en} } @article{FatkullinFoersterSchwarz1999, author = {Fatkullin, Mars N. and F{\"o}rster, Matthias and Schwarz, Udo}, title = {Irregularities of electron density and temperature in the day sector of the plasmasphere base during the summer season at high solar activity by observations of the aktivnyi satellite}, year = {1999}, abstract = {Based on the data of the Magion2 subsatellite of the Intercosmos24 satellite, an example of small-scale irregularities of the electron concentration with linear dimensions l ~ 100-300 m in the polar ion- osphere of the morning sector under field-aligned currents at altitudes of 1800-2030 km during the main phase of the magnetic storm of June 13, 1990 is presented. The dependence of the spectral index of the above small-scale irregularities on latitude is determined for the first time. Certain mechanisms of the generation of these small-scale irregularities are also qualitatively discussed.}, language = {en} } @book{BoeckmannSarkoezi1999, author = {B{\"o}ckmann, Christine and Sark{\"o}zi, Janos}, title = {The ill-posed inversion of multiwavelength lidar data by a hybrid method of variable projection}, series = {Preprint NLD}, volume = {53}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, issn = {1432-2935}, pages = {[7] S. : graph. Darst.}, year = {1999}, language = {en} } @article{SchwarzBenzKurthsetal.1993, author = {Schwarz, udo and Benz, Arnold O. and Kurths, J{\"u}rgen and Witt, Annette}, title = {Analysis of solar spike events by means of symbolic dynamics methods}, issn = {004-6361}, year = {1993}, abstract = {Using quantities of symbolic dynamics, such as mutual information, Shannon information and algorithmic complexity, we have searched for interrelations of spikes emitted simultaneously at different frequencies during the impulsive phase of a flare event. As the spikes are related to the flare energy release and are interpreted as emissions originating at different sites having different magnetic field strengths, any relation in frequency is interpretated as a relation in space. This approach is appropriate to characterize such spatio-temporal patterns, whereas the popular estimate of fractal dimensions can be applied to low-dimensional systems only. Depending on the energy release and emission processes, two types of fragmentation are possible: a scenario of global organization (spikes are emitted in a succession of similar events by the same system) or a scenario of local organization (many systems triggered by an initial event). Mutual information which is a generalization of correlation indicates a relation in frequency beyond the bandwidth of individual spikes. The scans in the spectrograms with large mutual information also show a low level of Shannon information and algorithmic complexity, indicating that the simultaneous appearance of spikes at other frequencies is not a completely stochastic phenomenon (white noise). It may be caused by a nonlinear deterministic system or by a Markov process. By means of mutual information we find a memory over frequency intervals up to 60 MHz. Shannon information and algorithmic complexity concern the mbox{whole} frequency region, i.e. the global source region. A global organization is also apparent in quasi-periodic changes of the Shannon information and algorithmic complexity in the range of 2 - 8 seconds. The finding is compatible with a scenario of local organization in which the information of one event spreads spatially and triggers further events at different places. The region is not an ensemble of independently flashing sources, each representing a system that cascades in energy after an initial trigger. On the contrary, there is a causal connection between the sources at any time. The analysis of the four spike events suggests that the structure in frequency is not stochastic but a process in which spikes at nearby locations are simultaneously triggered by a common exciter.}, language = {en} } @article{KurthsSchwarz1993, author = {Kurths, J{\"u}rgen and Schwarz, Udo}, title = {Application of techniques of nonlinear dynamics to SS Cyg}, isbn = {0-7503-0282-8}, year = {1993}, abstract = {We look for structural properties in the light curve of the dwarf nova SS Cyg by means of techniques from nonlinear dynamics. Applying the popular Grassberger-Procaccia procedure, Cannizzo and Goddings (1988) showed that there is no evidence for a low-dimensional attractor underlying this record. Because there are some hints for order in the light curve, we search for other signatures of deterministic systems. Therefore, we use other methods recently developed in this theory, such as local linear prediction and recurrence maps. Our main findings are: i] the prediction error grows exponentially during outburst phases, but via a power law in the quiescent states, ii] there are some rather regular patterns in this light curve which sometimes recur, but the recurrence is not regular. This leads to the following conclusions: i] The outburst dynamics shows a higher degree of order than the quiescent one. There are some hints for deterministic chaos in the outburst behavior. ii] The light curve is a complex mixture of deterministic and stochastic structures. The analysis presented in this paper shows that methods of nonlinear dynamics can be an efficient tool for the study of complex processes, even if there is no evidence for a low-dimensional attractor.}, language = {en} } @article{KurthsSchwarz1994, author = {Kurths, J{\"u}rgen and Schwarz, Udo}, title = {Chaos theory and radio emission}, year = {1994}, abstract = {The application of chaos theory has become popular to understand the nature of various features of solar activity because most of them are far from regular. The usual approach, however, that is basing on finding low- dimensional structures of the underlying processes seems to be successful only in a few exceptional cases, such as in rather coherent phenomena as coronal pulsations. It is important to note that most phenomena in solar radio emission are more complex. We present two kinds of techniques from nonlinear dynamics which can be useful to analyse such phenomena: i] Fragmentation processes observed in solar spike events are studied by means of symbolic dynamics methods. Different measures of complexity calculated from such observations reveal that there is some order in this fragmentation. ii] Bursts are a typical transient phenomenon. To study energization processes causing impulsive microwave bursts, the wavelet analysis is applied. It exhibits structural differences of the pre- and post-impulsive phase in cases where the power spectra of both are not distinct.}, language = {en} } @article{KurthsSchwarzWitt1995, author = {Kurths, J{\"u}rgen and Schwarz, Udo and Witt, Annette}, title = {Non-linear data analysis in solar radio astronomy}, year = {1995}, abstract = {We have discussed some tools from nonlinear dynamics which may help to analyze transient phenomena, such as solar bursts. The structure function known from turbulence theory is an appropriate method to find out some scaling behavior of fluctuations in time. More generally, the wavelet analysis, which is some generalization of the power spectrum, exhibits information on the location as well as the size of hidden characteristic features. Applying both techniques to microwave bursts, we have found some scaling properties that refer to the existence of hierarchic time structures. This is in good accordance with the electric circuit model for describing the flare-particle energization process.}, language = {en} } @article{VossTimmerKurths2004, author = {Voss, Henning U. and Timmer, Jens and Kurths, J{\"u}rgen}, title = {Modeling and identification of nonlinear systems}, issn = {0218-1274}, year = {2004}, language = {en} } @article{VossKurthsSchwarz1996, author = {Voss, Henning U. and Kurths, J{\"u}rgen and Schwarz, Udo}, title = {Reconstruction of grand minima of solar activity from radiocarbon data : linear and nonlinear signal analysis}, year = {1996}, abstract = {Using a special technique of data analysis, we have found out 34 grand minima of solar activity in a 7,700 years long C14 record. The method used rests on a proper filtering of the C14 record and the extrapolation of verifiable results for the later history back in time. Additionally, we have applied a method of nonlinear dynamics, the recurrence rate, to back up the results. Our findings are not contradictory to the record of grand minima by Eddy, but constitute a considerable extension. Hence, it has become possible to look closer at the validity of models. This way, we have tested esp. the model of Barnes et al. There are hints for that the grand minima might solely be driven by the 209--year period found in the C14 record.}, language = {en} } @article{TimmerSchwarzVossetal.2000, author = {Timmer, Jens and Schwarz, Udo and Voss, Henning U. and Wardinski, Ingo and Belloni, Tomaso and Hasinger, G{\"u}nther and VanDerKlis, Michael and Kurths, J{\"u}rgen}, title = {Linear and Nonlinear Time Series Analysis of the Black Hole Candidate Cygnus X-1}, year = {2000}, abstract = {We analyze the variability in the x-ray lightcurves of the black hole candidate Cygnus X-1 by linear and nonlinear time series analysis methods. While a linear model describes the overall second order properties of the observed data well, surrogate data analysis reveals a significant deviation from linearity. We discuss the relation between shot noise models usually applied to analyze these data and linear stochastic autoregressive models. We debate statistical and interpretational issues of surrogate data testing for the present context. Finally, we suggest a combination of tools from linear and nonlinear time series analysis methods as a procedure to test the predictions of astrophysical models on observed data.}, 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} }