13,325 research outputs found
Geometric and dynamic perspectives on phase-coherent and noncoherent chaos
Statistically distinguishing between phase-coherent and noncoherent chaotic
dynamics from time series is a contemporary problem in nonlinear sciences. In
this work, we propose different measures based on recurrence properties of
recorded trajectories, which characterize the underlying systems from both
geometric and dynamic viewpoints. The potentials of the individual measures for
discriminating phase-coherent and noncoherent chaotic oscillations are
discussed. A detailed numerical analysis is performed for the chaotic R\"ossler
system, which displays both types of chaos as one control parameter is varied,
and the Mackey-Glass system as an example of a time-delay system with
noncoherent chaos. Our results demonstrate that especially geometric measures
from recurrence network analysis are well suited for tracing transitions
between spiral- and screw-type chaos, a common route from phase-coherent to
noncoherent chaos also found in other nonlinear oscillators. A detailed
explanation of the observed behavior in terms of attractor geometry is given.Comment: 12 pages, 13 figure
Rhythmic dynamics and synchronization via dimensionality reduction : application to human gait
Reliable characterization of locomotor dynamics of human walking is vital to understanding the neuromuscular control of human locomotion and disease diagnosis. However, the inherent oscillation and ubiquity of noise in such non-strictly periodic signals pose great challenges to current methodologies. To this end, we exploit the state-of-the-art technology in pattern recognition and, specifically, dimensionality reduction techniques, and propose to reconstruct and characterize the dynamics accurately on the cycle scale of the signal. This is achieved by deriving a low-dimensional representation of the cycles through global optimization, which effectively preserves the topology of the cycles that are embedded in a high-dimensional Euclidian space. Our approach demonstrates a clear advantage in capturing the intrinsic dynamics and probing the subtle synchronization patterns from uni/bivariate oscillatory signals over traditional methods. Application to human gait data for healthy subjects and diabetics reveals a significant difference in the dynamics of ankle movements and ankle-knee coordination, but not in knee movements. These results indicate that the impaired sensory feedback from the feet due to diabetes does not influence the knee movement in general, and that normal human walking is not critically dependent on the feedback from the peripheral nervous system
Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System
Peer reviewedPublisher PD
Evaluation of selected recurrence measures in discriminating pre-ictal and inter-ictal periods from epileptic EEG data
7 pages, 4 figures Acknowledgement We are grateful to M. Riedl and G. Ansmann for fruitful discussions and critical comments on earlier versions of the manuscript. This work was supported by the Volkswagen Foundation (Grant Nos. 88461, 88462, 88463, 85390, 85391 and 85392).Peer reviewedPreprin
Quantifying sudden changes in dynamical systems using symbolic networks
We characterise the evolution of a dynamical system by combining two
well-known complex systems' tools, namely, symbolic ordinal analysis and
networks. From the ordinal representation of a time-series we construct a
network in which every node weights represents the probability of an ordinal
patterns (OPs) to appear in the symbolic sequence and each edges weight
represents the probability of transitions between two consecutive OPs. Several
network-based diagnostics are then proposed to characterize the dynamics of
different systems: logistic, tent and circle maps. We show that these
diagnostics are able to capture changes produced in the dynamics as a control
parameter is varied. We also apply our new measures to empirical data from
semiconductor lasers and show that they are able to anticipate the polarization
switchings, thus providing early warning signals of abrupt transitions.Comment: 18 pages, 9 figures, to appear in New Journal of Physic
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