Comparison of systems with complex behavior

From MaRDI portal
Publication:1888050

DOI10.1016/j.physd.2004.06.015zbMath1059.37072OpenAlexW2094686470MaRDI QIDQ1888050

Igor Mezić, Andrzej Banaszuk

Publication date: 22 November 2004

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2004.06.015



Related Items

A transfer operator approach to relativistic quantum wavefunction *, Lagrangian dynamic mode decomposition for construction of reduced-order models of advection-dominated phenomena, Operator-theoretic framework for forecasting nonlinear time series with kernel analog techniques, Koopman operator method for solution of generalized aggregate data inverse problems, Numerical methods to evaluate Koopman matrix from system equations*, Spatio-temporal Koopman decomposition, From large deviations to semidistances of transport and mixing: coherence analysis for finite Lagrangian data, Data Driven Modal Decompositions: Analysis and Enhancements, Koopman Linear Quadratic Regulator Using Complex Eigenfunctions for Nonlinear Dynamical Systems, Mesochronic classification of trajectories in incompressible 3D vector fields over finite times, On the computation of attractors for delay differential equations, Koopman Operator Family Spectrum for Nonautonomous Systems, Extreme phase sensitivity in systems with fractal isochrons, Modern Koopman Theory for Dynamical Systems, Generalizing Koopman Theory to Allow for Inputs and Control, Nonlinear observability via Koopman analysis: characterizing the role of symmetry, On the use of Fourier averages to compute the global isochrons of (quasi)periodic dynamics, Applied Koopmanism, Koopman analysis of the long-term evolution in a turbulent convection cell, Ergodic theory and visualization. II. Fourier mesochronic plots visualize (quasi)periodic sets, Linearization in the large of nonlinear systems and Koopman operator spectrum, Variants of dynamic mode decomposition: boundary condition, Koopman, and Fourier analyses, Spectral Properties of Pullback Operators on Vector Bundles of a Dynamical System, Deep Koopman model predictive control for enhancing transient stability in power grids, The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systems, Parsimony as the ultimate regularizer for physics-informed machine learning, Spectral complexity of directed graphs and application to structural decomposition, An incremental approach to online dynamic mode decomposition for time-varying systems with applications to EEG data modeling, Invariant Sets in Quasiperiodically Forced Dynamical Systems, Extended dynamic mode decomposition for two paradigms of non-linear dynamical systems, Nonlinear Model Order Reduction via Dynamic Mode Decomposition, High-dimensional time series prediction using kernel-based koopman mode regression, Prediction Accuracy of Dynamic Mode Decomposition, Ergodic Theory, Dynamic Mode Decomposition, and Computation of Spectral Properties of the Koopman Operator, Rigorous data‐driven computation of spectral properties of Koopman operators for dynamical systems, Dynamics of robust structures in turbulent swirling reacting flows, Growth rates for semiflows on Hausdorff spaces, Dynamic mode decomposition for analytic maps, Geometry of the ergodic quotient reveals coherent structures in flows, Isostables, isochrons, and Koopman spectrum for the action-angle representation of stable fixed point dynamics, Applied Koopman theory for partial differential equations and data-driven modeling of spatio-temporal systems, Delay-coordinate maps, coherence, and approximate spectra of evolution operators, Spectral analysis of nonlinear flows, Computational hydrodynamic stability and flow control based on spectral analysis of linear operators, On convergence of extended dynamic mode decomposition to the Koopman operator, Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator, Randomized model order reduction, Spectral properties of dynamical systems, model reduction and decompositions, Convex computation of extremal invariant measures of nonlinear dynamical systems and Markov processes, Koopman operator framework for time series modeling and analysis, Koopman operator spectrum for random dynamical systems, On robust computation of Koopman operator and prediction in random dynamical systems, Spectrum of the Koopman operator, spectral expansions in functional spaces, and state-space geometry, Geometric considerations of a good dictionary for Koopman analysis of dynamical systems: cardinality, ``primary eigenfunction, and efficient representation, On Matching, and Even Rectifying, Dynamical Systems through Koopman Operator Eigenfunctions, Reproducing kernel Hilbert space compactification of unitary evolution groups, Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools, Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control, A non-equilibrium analysis and control framework for active queue management, Uncertainty propagation in dynamical systems, Multiresolution Dynamic Mode Decomposition, Taxicab geometry in table of higher-order elements, Searching turbulence for periodic orbits with dynamic mode decomposition, Data-driven spectral analysis of the Koopman operator, On the Approximation of Koopman Spectra of Measure-Preserving Flows, Delay-coordinate maps and the spectra of Koopman operators, Koopman mode expansions between simple invariant solutions, On the Approximation of Koopman Spectra for Measure Preserving Transformations, Existence and uniqueness of global Koopman eigenfunctions for stable fixed points and periodic orbits, Koopman spectra in reproducing kernel Hilbert spaces, Data-driven spectral decomposition and forecasting of ergodic dynamical systems, Spatiotemporal pattern extraction by spectral analysis of vector-valued observables, Explicit invariant manifolds and specialised trajectories in a class of unsteady flows, Ergodic theory and visualization. I. Mesochronic plots for visualization of ergodic partition and invariant sets, Feedback control of cavity flow oscillations using simple linear models, Deep learning models for global coordinate transformations that linearise PDEs, Residual dynamic mode decomposition: robust and verified Koopmanism, Global Isochrons and Phase Sensitivity of Bursting Neurons



Cites Work