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(11)
Bifurcation Analysis
Dynamic Properties
Dynamic System
Euclidean Space
Optimal Transportation
Phase Space
Probability Distribution
Statistical Techniques
Time Series
Time Series Analysis
Wasserstein Distance
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Wasserstein distances in the analysis of time series and dynamical systems
Wasserstein distances in the analysis of time series and dynamical systems,10.1016/j.physd.2010.08.005,Physica Dnonlinear Phenomena,Michael Muskulus,
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Wasserstein distances in the analysis of time series and dynamical systems
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Michael Muskulus
,
Sjoerd VerduynLunel
A new approach based on Wasserstein distances, which are numerical costs of an
optimal transportation
problem, allows us to analyze nonlinear phenomena in a robust manner. The longterm behavior is reconstructed from time series, resulting in a
probability distribution
over phase space. Each pair of probability distributions is then assigned a numerical distance that quantifies the differences in their dynamical properties. From the totality of all these distances a lowdimensional representation in a
Euclidean space
is derived, in which the
time series
can be classified and statistically analyzed. This representation shows the functional relationships between the dynamical systems under study. It allows us to assess synchronization properties and also offers a new way of numerical bifurcation analysis.The
statistical techniques
for this distancebased analysis of dynamical systems are presented, filling a gap in the literature, and their application is discussed in a few examples of datasets arising in physiology and neuroscience, and in the wellknown Hénon system.
Journal:
Physica Dnonlinear Phenomena  PHYSICA D
, vol. 240, no. 1, pp. 4558, 2011
DOI:
10.1016/j.physd.2010.08.005
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Citation Context
(1)
...of variability within the system calculated as the power of RRI oscillations in various frequency ranges. The overall amount of variability in these ranges of the RRI PSD is an obviously essential dimension of neurocardiac dynamics, but unlikely the only dimension, especially if one considers the possibility that RRI PSD dynamics can change qualitatively and nonlinearly in response to perturbation
...
Marsha E. Bates
,
et al.
The Redistribution of Power: Neurocardiac Signaling, Alcohol and Gende...
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Citations
(1)
The Redistribution of Power: Neurocardiac Signaling, Alcohol and Gender
Marsha E. Bates
,
Jennifer F. Buckman
,
Evgeny G. Vaschillo
,
Vladimir A. Fonoberov
,
Maria Fonoberova
,
Bronya Vaschillo
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EunYoung Mun
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