Parameters of the fractional Fokker-Planck equation (2008)
Denisov, S. I., Hänggi, Peter, Kantz, Holger
We study the connection between the parameters of the fractional Fokker-Planck equation, which is associated with the overdamped Langevin equation driven by noise with heavy-tailed increments, and...
Optimal Markov Approximations and Generalized Embeddings (2008)
Holstein, Detlef, Kantz, Holger
Based on information theory, we present a method to determine an optimal Markov approximation for modelling and prediction from time series data. The method finds a balance between minimal modelling...
Return interval distribution of extreme events and long term memory (2008)
Santhanam, M. S., Kantz, Holger
The distribution of recurrence times or return intervals between extreme events is important to characterize and understand the behavior of physical systems and phenomena in many disciplines. It is...
September 10, 1998 Fitting Partial Differential Equations to Space-Time-Dynamics (2008)
Abstract The partial differential equations (PDE's) governing the dynamics of reaction-diffusion systems are reconstructed from data representing the spatially extended systems. The fitted...
Bahraminasab, Alireza, Ghasemi, Fatemeh, Stefanovska, Aneta, McClintock, Peter V. E., Kantz, Holger
We introduce a directionality index for a time series based on a comparison of neighboring values. It can distinguish unidirectional from bidirectional coupling, as well as reveal and quantify...
Identifying and modelling delay feedback systems (2007)
Rainer Hegger, Martin J. Bunner, Holger Kantz, Antonino Giaquinta
Systems with delayed feedback can possess chaotic attractors with extremely high dimension, even if only a few physical degrees of freedom are involved. We propose a state space reconstruction from...
Rainer Hegger, Holger Kantz, Frank Schmuser, Martin Diestelhorst, Ralf-peter Kapsch, Horst Beige
through nonlinear time series analysis
LETTER TO THE EDITOR Some considerations on Poincare (2007)
maps for chaotic flows
Some considerations on Poincaré maps for chaotic flows (2007)
. The standard way to reduce a flow to a time--discrete dynamical system is by the technique of the Poincar'e surface of section. We discuss the relationship between Poincar'e maps obtained...
Reconstruction of the Dynamics of Noisy Multivariate Time Series (2007)
Rainer Hegger, Lars Jaeger, Holger Kantz
We generalize the multi step prediction cost function for an unbiased reconstruction of the dynamics for noisy time series recently proposed for the case of scalar time series (which requires a...
Noise Reduction for Experimental Data (2007)
We introduce an algorithm for nonlinear noise reduction which is based on locally linear fits to the nonlinear dynamics. We claim that it is both robust and flexible enough to apply it to a variety...
Holger Kantz, Wolfram Just, Nilüfer Baba, Katrin Gelfert, Anja Rieger
We show in detail how methods of time series analysis such as dimension and entropy estimates support the idea that fast low-dimensional chaos can be modeled properly by noise. Motivated by this...
Hypothesis of strong chaos and anomalous diffusion in coupled symplectic maps (2006)
Altmann, Eduardo G., Kantz, Holger
We investigate the high dimensional Hamiltonian chaotic dynamics in $N$ coupled area-preserving maps. We show the existence of an enhanced trapping regime caused by trajectories performing a random...
Precursors of extreme increments (2006)
Hallerberg, Sarah, Altmann, Eduardo G., Holstein, Detlef, Kantz, Holger
We investigate precursors and predictability of extreme increments in a time series. The events we are focusing on consist in large increments within successive time steps. We are especially...
Stickiness in Hamiltonian systems: from sharply divided to hierarchical phase space (2006)
Altmann, Eduardo G., Motter, Adilson E., Kantz, Holger
We investigate the dynamics of chaotic trajectories in simple yet physically important Hamiltonian systems with non-hierarchical borders between regular and chaotic regions with positive measures. We...
Reactions to extreme events: moving threshold model (2005)
Altmann, Eduardo G., Hallerberg, Sarah, Kantz, Holger
In spite of precautions to avoid the harmful effects of extreme events, we experience recurrently phenomena that overcome the preventive barriers. These barriers usually increase drastically right...
Improvement of speech recognition by nonlinear noise reduction (2005)
Urbanowicz, Krzysztof, Kantz, Holger
The success of nonlinear noise reduction applied to a single channel recording of human voice is measured in terms of the recognition rate of a commercial speech recognition program in comparison to...
Effective dynamics in Hamiltonian systems with mixed phase space (2005)
Motter, Adilson E., Grebogi, Celso, Kantz, Holger
An adequate characterization of the dynamics of Hamiltonian systems at physically relevant scales has been largely lacking. Here we investigate this fundamental problem and we show that the...
Recurrence time analysis, long-term correlations, and extreme events (2005)
Altmann, Eduardo G., Kantz, Holger
The recurrence times between extreme events have been the central point of statistical analyses in many different areas of science. Simultaneously, the Poincar\'e recurrence time has been extensively...
Stickiness in mushroom billiards (2005)
Altmann, Eduardo G., Motter, Adilson E., Kantz, Holger
We investigate dynamical properties of chaotic trajectories in mushroom billiards. These billiards present a well-defined simple border between a single regular region and a single chaotic component....
Anti-deterministic behavior of discrete systems that are less predictable than noise (2004)
Urbanowicz, Krzysztof, Kantz, Holger, Holyst, Janusz A.
We present a new type of deterministic dynamical behaviour that is less predictable than white noise. We call it anti-deterministic (AD) because time series corresponding to the dynamics of such...
Complex dynamics in simple systems with seasonal parameter oscillations (2003)
Juarez, L. Hector, Kantz, Holger, Martinez, Oscar, Ramos, Eduardo, Rechtman, Raul
We study systems with periodically oscillating parameters that can give way to complex periodic or non periodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov...
Elimination of Fast Chaotic Degrees of Freedom: On the accuracy of the Born approximation (2003)
Wolfram Just, Katrin Gelfert, Nilüfer Baba, Anja Riegert, Holger Kantz
We apply standard projection operator techniques known from nonequilibrium statistical mechanics to eliminate fast chaotic degrees of freedom in a low{dimensional dynamical system. Through the usual...
Enlarged scaling ranges for the KS-entropy and the information dimension (2002)
Kantz, Holger, Schürmann, Thomas
Numerical estimates of the Kolmogorov-Sinai entropy based on a finite amount of data decay towards zero in the relevant limits. Rewriting differences of block entropies as averages over decay rates,...
Stochastic modelling: Replacing fast degrees of freedom by noise (2001)
Wolfram Just, Holger Kantz, Christian Rödenbeck, Mario Helm
In systems with time scale separation, where the fast degrees of freedom exhibit chaotic motion, the latter are replaced by suitable stochastic processes. A projection technique is employed to derive...
Analysis of Vocal Disorders in a Feature Space (2000)
Matassini, Lorenzo, Hegger, Rainer, Kantz, Holger, Manfredi, Claudia
This paper provides a way to classify vocal disorders for clinical applications. This goal is achieved by means of geometric signal separation in a feature space. Typical quantities from chaos theory...
Local estimates for entropy densities in coupled map lattices (2000)
Olbrich, Eckehard, Hegger, Rainer, Kantz, Holger
We present a method to derive an upper bound for the entropy density of coupled map lattices with local interactions from local observations. To do this, we use an embedding technique being a...
Identifying and modelling delay feedback systems (1999)
Hegger, Rainer, Bünner, Martin J., Kantz, Holger, Giaquinta, Antonino
Systems with delayed feedback can possess chaotic attractors with extremely high dimension, even if only a few physical degrees of freedom are involved. We propose a state space reconstruction from...
Identification and characterization of systems with delayed feedback: (I) Theory and tools (1999)
Bünner, Martin J., Ciofini, Marco, Giaquinta, Antonino, Hegger, Rainer, Kantz, Holger, Meucci, Riccardo, ...
High-dimensional chaos displayed by multi-component systems with a single time-delayed feedback is shown to be accessible to time series analysis of a scalar variable only. The mapping of the...
Practical implementation of nonlinear time series methods: The TISEAN package (1998)
Hegger, Rainer, Kantz, Holger, Schreiber, Thomas
Nonlinear time series analysis is becoming a more and more reliable tool for the study of complicated dynamics from measurements. The concept of low-dimensional chaos has proven to be fruitful in the...
The human ECG - nonlinear deterministic versus stochastic aspects (1998)
Kantz, Holger, Schreiber, Thomas
We discuss aspects of randomness and of determinism in electrocardiographic signals. In particular, we take a critical look at attempts to apply methods of nonlinear time series analysis derived from...
The Transition From Deterministic Chaos to a Stochastic Process (1998)
Holger Kantz, Eckehard Olbrich
Deterministic dynamical systems of Langevin type recently introduced by Beck & Roepsdorf [Physica 145 A (1987) 1] generate Langevin dynamics in a suitable limit. We discuss the transition from...
Nonlinear Projective Filtering I: Background in Chaos Theory (1998)
Holger Kantz, Thomas Schreiber
We derive a locally projective noise reduction scheme for nonlinear time series using concepts from deterministic dynamical systems, or chaos theory. We will demonstrate its effectiveness with an...
The human ECG - nonlinear deterministic versus stochastic aspects (1998)
Holger Kantz, Thomas Schreiber
this article we discuss exclusively electrocardiographic (ECG) data [13] measured with surface electrodes. Some arguments can be carried over to invasive recordings as well. The ECG signal reflects...
Nonlinear Projective Filtering II: Application To Real Time Series (1998)
Thomas Schreiber, Holger Kantz
We discuss applications of nonlinear filtering of time series by locally linear phase space projections. Noise can be reduced whenever the error due to the manifold approximation is smaller than the...
Embedding of Sequences of Time Intervals (1997)
Times series obtained from dynamical systems can be converted into sequences of time intervals between relevant events. We show that under quite general conditions time intervals are phase space...
Correlation Dimension of Intermittent Signals (1997)
Rainer Hegger, Holger Kantz, Eckehard Olbrich
We investigate the breaking of proper self similarity of attractors in the presence of intermittency. We show that this can lead to dramatically too small values of the numerically estimated...
Observing and predicting chaotic signals: Is 2% noise too much? (1996)
Thomas Schreiber, Holger Kantz
: We discuss the influence of noise on the analysis of complex time series data. How harmful it is depends on the nature of the noise, the complexity of the signal and on the application in mind. We...
Noise in Chaotic Data: Diagnosis and Treatment (1995)
Thomas Schreiber, Holger Kantz
: A prominent limiting factor in the analysis of chaotic time series are measurement errors in the data. We show that this influence can be quite severe, depending on the nature of the noise, the...
Return interval distribution of extreme events and long term memory
The distribution of recurrence times or return intervals between extreme events is important to characterize and understand the behavior of physical systems and phenomena in many disciplines. It is...