@article{ZiehmannSmithKurths1999,
  author    = {Ziehmann, Christine and Smith, L. and Kurths, J{\"u}rgen},
  title     = {The bootstrap and lyapunov exponents in deterministic chaos},
  year      = {1999},
  language  = {en}
}
@article{SmithZiehmannFraedrich1999,
  author    = {Smith, L. and Ziehmann, Christine and Fraedrich, K.},
  title     = {Uncertainty dynamics and predictability in chaotic systems},
  year      = {1999},
  language  = {en}
}
@article{ZiehmannSmithKurths2000,
  author    = {Ziehmann, Christine and Smith, Leonard A. and Kurths, J{\"u}rgen},
  title     = {Localized Lyapunov exponents and the prediction of predictability},
  year      = {2000},
  language  = {en}
}
@article{WesselVossMalbergetal.2000,
  author    = {Wessel, Niels and Voss, Andreas and Malberg, Hagen and Ziehmann, Christine and Voss, Henning U. and Schirdewan, Alexander and Meyerfeldt, Udo and Kurths, J{\"u}rgen},
  title     = {Nonlinear analysis of complex phenomena in cardiological data},
  year      = {2000},
  abstract  = {The main intention of this contribution is to discuss different nonlinear approaches to heart rate and blood pressure variability analysis for a better understanding of the cardiovascular regulation. We investigate measures of complexity which are based on symbolic dynamics, renormalised entropy and the finite time growth rates. The dual sequence method to estimate the baroreflex sensitivity and the maximal correlation method to estimate the nonlinear coupling between time series are employed for analysing bivariate data. The latter appears to be a suitable method to estimate the strength of the nonlinear coupling and the coupling direction. Heart rate and blood pressure data from clinical pilot studies and from very large clinical studies are analysed. We demonstrate that parameters from nonlinear dynamics are useful for risk stratification after myocardial infarction, for the prediction of life-threatening cardiac events even in short time series, and for modelling the relationship between heart rate and blood pressure regulation. These findings could be of importance for clinical diagnostics, in algorithms for risk stratification, and for therapeutic and preventive tools of next generation implantable cardioverter defibrillators.},
  language  = {en}
}
@article{WesselZiehmannKurthsetal.2000,
  author    = {Wessel, Niels and Ziehmann, Christine and Kurths, J{\"u}rgen and Meyerfeldt, Udo and Schirdewan, Alexander and Voss, Andreas},
  title     = {Short-term forecasting of life-threatening cardiac arrhythmias based on symbolic dynamics and finite-time growth rates},
  year      = {2000},
  abstract  = {Ventricular tachycardia or fibrillation (VT-VF) as fatal cardiac arrhythmias are the main factors triggering sudden cardiac death. The objective of this study is to find early signs of sustained VT-VF in patients with an implanted cardioverter-defibrillator (ICD). These devices are able to safeguard patients by returning their hearts to a normal rhythm via strong defibrillatory shocks; additionally, they store the 1000 beat-to-beat intervals immediately before the onset of a life-threatening arrhythmia. We study these 1000 beat-to-beat intervals of 17 chronic heart failure ICD patients before the onset of a life-threatening arrhythmia and at a control time, i.e., without a VT-VF event. To characterize these rather short data sets, we calculate heart rate variability parameters from the time and frequency domain, from symbolic dynamics as well as the finite-time growth rates. We find that neither the time nor the frequency domain parameters show significant differences between the VT-VF and the control time series. However, two parameters from symbolic dynamics as well as the finite-time growth rates discriminate significantly both groups. These findings could be of importance in algorithms for next generation ICD's to improve the diagnostics and therapy of VT-VF.},
  language  = {en}
}