Detecting strange attractors in turbulence

  title={Detecting strange attractors in turbulence},
  author={Floris Takens},
Empirical Dynamic Modeling
Empirical dynamic modeling (EDM) is an emerging non-parametric framework for modeling nonlinear dynamic systems. EDM is based on the mathematical theory of reconstructing attractor manifolds fromExpand
Persistent Homology of Complex Networks for Dynamic State Detection
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Analysis of Flow Dynamics in the High-Flux Gas-Solid Riser Using Trajectory Distances across Attractors Reconstructed from Solid Concentration Signals
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Complex Systems Research in Educational Psychology: Aligning Theory and Method
A philosophically and theoretically sourced definition of complex systems research organized around complex, dynamic, and emergent ontological characteristics that is useful and appropriate for educational psychology is outlined. Expand
Quantitatively Characterizing Drug-Induced Arrhythmic Contractile Motions of Human Stem Cell-Derived Cardiomyocytes.
This paper generated contractile motion data from beating hiPSC-CMs using motion tracking software based on optical flow analysis, and implemented a computational algorithm, phase space reconstruction (PSR), to derive parameters (embedding, regularity, and fractal dimensions) to further characterize the dynamic nature of the cardiac contractile motions. Expand
Data Analysis Methods using Persistence Diagrams
A new distance is introduced on the space of persistence diagrams, and it is shown that it is useful in detecting changes in geometry and topology, which is essential for the supervised learning problem. Expand
Selección de Características Mediante un Algoritmo Genético para el Diagnóstico de Caoticidad en Series de Tiempo Usando un Clasificador con Redes Neuronales
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Physiological Signal Analysis: A Topo-Geometric Perspective.
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In the present thesis two main results are presented. The first is a study of the statistical properties of the finite-time maximum Lyapunov exponent determined out of a time series by using theExpand
Analog Forecasting with Dynamics-Adapted Kernels
Analog forecasting is a nonparametric technique introduced by Lorenz in 1969 which predicts the evolution of states of a dynamical system (or observables defined on the states) by following theExpand


A dynamical system consists of a smooth vectorfield defined on a differentiable manifold, and a smooth mapping from the manifold to the real numbers. The vectorfield represents the dynamics of aExpand
2[he pre-turbutent transitions and flows of a viscous fluid between concentric rotating cylinders
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Xhe dimension of the strange attractor for a class of difference systems, preprint
  • Xhe dimension of the strange attractor for a class of difference systems, preprint
  • 1980
Dynamical instabilities and the transition to chaotic Taylor vortex flow
We have used the technique of laser-Doppler velocimetry to study the transition to turbulence in a fluid contained between concentric cylinders with the inner cylinder rotating. The experiment wasExpand
Geometry from the time series, preprint
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  • 1979
Ergodic Theory on Compact Spaces
Measure-theoretic dynamical systems.- Measures on compact metric spaces.- Invariant measures for continuous tranformations.- Time averages.- Ergodicity.- Mixing and transitivity.- Shifts andExpand
The Hopf Bifurcation and Its Applications
The goal of these notes is to give a reasonably complete, although not exhaustive, discussion of what is commonly referred to as the Hopf bifurcation with applications to specific problems, includingExpand