@unpublished{WittNeimanKurths1997,
  author    = {Witt, Annette and Neiman, Alexander and Kurths, J{\"u}rgen},
  title     = {Characterizing the dynamics of stochastic bistable systems by measures of complexity},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14556},
  year      = {1997},
  abstract  = {The dynamics of noisy bistable systems is analyzed by means of Lyapunov exponents and measures of complexity. We consider both the classical Kramers problem with additive white noise and the case when the barrier fluctuates due to additional external colored noise. In case of additive noise we calculate the Lyapunov exponents and all measures of complexity analytically as functions of the noise intensity resp. the mean escape time. For the problem of fluctuating barrier the usual description of the dynamics with the mean escape time is not sufficient. The application of the concept of measures of complexity allows to describe the structures of motion in more detail. Most complexity measures sign the value of correlation time at which the phenomenon of resonant activation occurs with an extremum.},
  language  = {en}
}
@unpublished{WittKurthsKrauseetal.1994,
  author    = {Witt, Annette and Kurths, J{\"u}rgen and Krause, F. and Fischer, K.},
  title     = {On the validity of a model for the reversals of the Earth's magnetic field},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13460},
  year      = {1994},
  abstract  = {We have used techniques of nonlinear dynamics to compare a special model for the reversals of the Earth's magnetic field with the observational data. Although this model is rather simple, there is no essential difference to the data by means of well-known characteristics, such as correlation function and probability distribution. Applying methods of symbolic dynamics we have found that the considered model is not able to describe the dynamical properties of the observed process. These significant differences are expressed by algorithmic complexity and Renyi information.},
  language  = {en}
}
@unpublished{VossKurthsSchwarz1996,
  author    = {Voss, Henning and Kurths, J{\"u}rgen and Schwarz, Udo},
  title     = {Reconstruction of grand minima of solar activity from Delta 14 C data : linear and nonlinear signal analysis},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14083},
  year      = {1996},
  abstract  = {Using a special technique of data analysis, we have found out 34 grand minima of solar activity obtained from a 7,700 years long Δ14C record. The method used rests on a proper filtering of the Δ14C record and the extrapolation of verifiable results for the later history back in time. Additionally, we use a method of nonlinear dynamics, the recurrence rate, to back up the results. Our findings are not contradictory to the record of solar maxima resp. minima by Eddy [5], but constitute a considerable extension. Hence, it has become possible to look closer at the validity of models. This way, we have tested several models for solar activity, esp. the model of Barnes et al. [1]. There are hints for that the grand minima might solely be driven by the 209 year period found in the Δ14C record.},
  language  = {en}
}
@unpublished{ThiessenhusenEspositoKurthsetal.1995,
  author    = {Thiessenhusen, Kai-Uwe and Esposito, Larry W. and Kurths, J{\"u}rgen and Spahn, Frank},
  title     = {Detection of hidden resonances in Saturn's B-ring},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13618},
  year      = {1995},
  abstract  = {The Voyager 2 Photopolarimeter experiment has yielded the highest resolved data of Saturn's rings, exhibiting a wide variety of features. The B-ring region between 105000 km and 110000 km distance from Saturn has been investigated. It has a high matter density and contains no significance features visible by eye. Analysis with statistical methods has let us to the detection of two significant events. These features are correlated with the inner 3:2 resonances of the F-ring shepherd satellites Pandora and Prometheus, and may be evidence of large ring paricles caught in the corotation resonances.},
  language  = {en}
}
@misc{ThielRomanoKurthsetal.2006,
  author    = {Thiel, Marco and Romano, Maria Carmen and Kurths, J{\"u}rgen and Rolfs, Martin and Kliegl, Reinhold},
  title     = {Generating Surrogates from Recurrences},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-56906},
  year      = {2006},
  abstract  = {In this paper we present an approach to recover the dynamics from recurrences of a system and then generate (multivariate) twin surrogate (TS) trajectories. In contrast to other approaches, such as the linear-like surrogates, this technique produces surrogates which correspond to an independent copy of the underlying system, i. e. they induce a trajectory of the underlying system visiting the attractor in a different way. We show that these surrogates are well suited to test for complex synchronization, which makes it possible to systematically assess the reliability of synchronization analyses. We then apply the TS to study binocular fixational movements and find strong indications that the fixational movements of the left and right eye are phase synchronized. This result indicates that there might be one centre only in the brain that produces the fixational movements in both eyes or a close link between two centres.},
  language  = {en}
}
@misc{ThielRomanoKurthsetal.2006,
  author    = {Thiel, Marco and Romano, Maria Carmen and Kurths, J{\"u}rgen and Rolfs, Martin},
  title     = {Twin Surrogates to Test for Complex Synchronisation},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-57231},
  year      = {2006},
  abstract  = {We present an approach to generate (multivariate) twin surrogates (TS) based on recurrence properties. This technique generates surrogates which correspond to an independent copy of the underlying system, i. e. they induce a trajectory of the underlying system starting at different initial conditions. We show that these surrogates are well suited to test for complex synchronisation and exemplify this for the paradigmatic system of R¨ossler oscillators. The proposed test enables to assess the statistical relevance of a synchronisation analysis from passive experiments which are typical in natural systems.},
  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}
}
@misc{LiMeiXuetal.2020,
  author    = {Li, Yongge and Mei, Ruoxing and Xu, Yong and Kurths, J{\"u}rgen and Duan, Jinqiao and Metzler, Ralf},
  title     = {Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {974},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-47454},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-474542},
  pages     = {28},
  year      = {2020},
  abstract  = {This work focuses on the dynamics of particles in a confined geometry with position-dependent diffusivity, where the confinement is modelled by a periodic channel consisting of unit cells connected by narrow passage ways. We consider three functional forms for the diffusivity, corresponding to the scenarios of a constant (D ₀), as well as a low (D ₘ) and a high (D d) mobility diffusion in cell centre of the longitudinally symmetric cells. Due to the interaction among the diffusivity, channel shape and external force, the system exhibits complex and interesting phenomena. By calculating the probability density function, mean velocity and mean first exit time with the It{\^o} calculus form, we find that in the absence of external forces the diffusivity D d will redistribute particles near the channel wall, while the diffusivity D ₘ will trap them near the cell centre. The superposition of external forces will break their static distributions. Besides, our results demonstrate that for the diffusivity D d, a high dependence on the x coordinate (parallel with the central channel line) will improve the mean velocity of the particles. In contrast, for the diffusivity D ₘ, a weak dependence on the x coordinate will dramatically accelerate the moving speed. In addition, it shows that a large external force can weaken the influences of different diffusivities; inversely, for a small external force, the types of diffusivity affect significantly the particle dynamics. In practice, one can apply these results to achieve a prominent enhancement of the particle transport in two- or three-dimensional channels by modulating the local tracer diffusivity via an engineered gel of varying porosity or by adding a cold tube to cool down the diffusivity along the central line, which may be a relevant effect in engineering applications. Effects of different stochastic calculi in the evaluation of the underlying multiplicative stochastic equation for different physical scenarios are discussed.},
  language  = {en}
}
@unpublished{KurthsVossWittetal.1994,
  author    = {Kurths, J{\"u}rgen and Voss, A. and Witt, Annette and Saparin, P. and Kleiner, H. J. and Wessel, Niels},
  title     = {Quantitative analysis of heart rate variability},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13470},
  year      = {1994},
  abstract  = {In the modern industrialized countries every year several hundred thousands of people die due to the sudden cardiac death. The individual risk for this sudden cardiac death cannot be defined precisely by common available, non-invasive diagnostic tools like Holter-monitoring, highly amplified ECG and traditional linear analysis of heart rate variability (HRV). Therefore, we apply some rather unconventional methods of nonlinear dynamics to analyse the HRV. Especially, some complexity measures that are basing on symbolic dynamics as well as a new measure, the renormalized entropy, detect some abnormalities in the HRV of several patients who have been classified in the low risk group by traditional methods. A combination of these complexity measures with the parameters in the frequency domain seems to be a promising way to get a more precise definition of the individual risk. These findings have to be validated by a representative number of patients.},
  language  = {en}
}
@unpublished{KurthsPikovskijScheffczyk1994,
  author    = {Kurths, J{\"u}rgen and Pikovskij, Arkadij and Scheffczyk, Christian},
  title     = {Roughening interfaces in deterministic dynamics},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13447},
  year      = {1994},
  abstract  = {Two deterministic processes leading to roughening interfaces are considered. It is shown that the dynamics of linear perturbations of turbulent regimes in coupled map lattices is governed by a discrete version of the Kardar-Parisi-Zhang equation. The asymptotic scaling behavior of the perturbation field is investigated in the case of large lattices. Secondly, the dynamics of an order-disorder interface is modelled with a simple two-dimensional coupled map lattice, possesing a turbulent and a laminar state. It is demonstrated, that in some range of parameters the spreading of the turbulent state is accompanied by kinetic roughening of the interface.},
  language  = {en}
}