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Understanding the interplay of order and disorder in chaotic systems is a central challenge in modern quantitative science.
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Measuring chaos in the brain: a tutorial review of nonlinear dynamical EEG analysis
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Extraction of dynamical equations from chaotic data
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Nonlinear prediction as a way of distinguishing chaos from random fractal sequences
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Using small perturbations to control chaos
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Genetic programming as a Darwinian invention machine
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A course in robust control theory: A convex approach
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Physiobank, physiotoolkit, and physionet components of a new research resource for complex physiologic signals
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Analysis of a sleep-dependent neuronal feedback loop: the slow-wave microcontinuity of the eeg
Applied Koopmanism a)
M. Budišić, R. Mohr, and I. Mezić · 2012
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Variants of dynamic mode decomposition: Boundary condition, Koopman, and Fourier analyses
K. K. Chen, J. H. Tu, and C. W. Rowley · 2012
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Between order and chaos
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Nonlinear Laplacian spectral analysis for time series with intermittency and low-frequency variability
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Physics constrained nonlinear regression models for time series
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Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics
W. S. Koon, M. W. Lo, J. E. Marsden, and S. D. Ross · 2000
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Noisy clockwork: time series analysis of population fluctuations in animals
O. N. Bjørnstad and B. T. Grenfell · 2001
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The algorithms behind GAIO—set oriented numerical methods for dynamical systems
M. Dellnitz, G. Froyland, and O. Junge · 2001
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M. Dellnitz and O. Junge · 2002
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Equation-free, coarse-grained multiscale computation: Enabling microscopic simulators to perform system-level analysis
I. G. Kevrekidis, C. W. Gear, J. M. Hyman, P. G. Kevrekidis, O. Runborg, and C. Theodoropoulos · 2003
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Non-linear analysis of EEG signals at various sleep stages
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Koopman-mode decomposition of the cylinder wake
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Linearization in the large of nonlinear systems and Koopman operator spectrum
Y. Lan and I. Mezić · 2013
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Analysis of fluid flows via spectral properties of the Koopman operator
I. Mezić · 2013
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Compressed modes for variational problems in mathematics and physics
V. Ozoliņš, R. Lai, R. Caflisch, and S. Osher · 2013
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Statistically accurate low-order models for uncertainty quantification in turbulent dynamical systems
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Sparse dynamics for partial differential equations
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Compressive sensing and low-rank libraries for classification of bifurcation regimes in nonlinear dynamical systems
S. L. Brunton, J. H. Tu, I. Bright, and J. N. Kutz · 2014
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Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model
W. Cousins and T. P. Sapsis · 2014
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A computational method to extract macroscopic variables and their dynamics in multiscale systems
G. Froyland, G. A. Gottwald, and A. Hammerlindl · 2014
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The optimal hard threshold for singular values is 4 / 3 4/\sqrt{3}
M. Gavish and D. L. Donoho · 2014
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Cluster-based reduced-order modelling of a mixing layer
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On the compressive spectral method
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Conceptual dynamical models for turbulence
A. J. Majda and Y. Lee · 2014
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Exploiting sparsity and equation-free architectures in complex systems (invited review)
J. L. Proctor, S. L. Brunton, B. W. Brunton, and J. N. Kutz · 2014
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On dynamic mode decomposition: theory and applications
J. H. Tu, C. W. Rowley, D. M. Luchtenburg, S. L. Brunton, and J. N. Kutz · 2014
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Closed-loop turbulence control: Progress and challenges
S. L. Brunton and B. R. Noack · 2015
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Data-driven spectral decomposition and forecasting of ergodic dynamical systems
D. Giannakis · 2015
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Delay differential analysis of electroencephalographic data
Claudia Lainscsek, Manuel E Hernandez, Howard Poizner, and Terrence J Sejnowski · 2015
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A data-driven approximation of the Koopman operator: extending dynamic mode decomposition
M. O. Williams, I. G. Kevrekidis, and C. W. Rowley · 2015
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Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling
H. Ye, R. J. Beamish, S. M. Glaser, S. C. H. Grant, C.-H. Hsieh, L. J. Richards, J. T. Schnute, and G. Sugihara · 2015
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