A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors
DOI10.1137/19M1247139zbMath1439.37082arXiv1902.08074MaRDI QIDQ4961116
Adrian Ziessler, Raphael Gerlach, Michael Dellnitz, Bruno Eckhardt
Publication date: 21 April 2020
Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1902.08074
attractorsshear flowsbifurcation analysispath following methodset-oriented numericsCharney-DeVore model
Shear flows and turbulence (76F10) Attractors of solutions to ordinary differential equations (34D45) Dynamical aspects of attractors and their bifurcations (37G35) Computational methods for bifurcation problems in dynamical systems (37M20) Numerical bifurcation problems (65P30) Transition to turbulence (76F06) Computational methods for attractors of dynamical systems (37M22)
Uses Software
Cites Work
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- On the computation of attractors for delay differential equations
- Lower semicontinuity of attractors of gradient systems and applications
- Coherent sets for nonautonomous dynamical systems
- Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
- Numerical computation of heteroclinic orbits
- Global bifurcations and chaos. Analytical methods
- Singularities and groups in bifurcation theory. Volume II
- The Couette-Taylor problem
- A subdivision algorithm for the computation of unstable manifolds and global attractors
- Stability and transition in shear flows
- The symmetry perspective. From equilibrium to chaos in phase space and physical space
- Transition to turbulence in shear flows
- Set oriented computation of transport rates in 3-degree of freedom systems: the Rydberg atom in crossed fields
- Combinatorial-topological framework for the analysis of global dynamics
- A Set-Oriented Numerical Approach for Dynamical Systems with Parameter Uncertainty
- Interactive Initialization and Continuation of Homoclinic and Heteroclinic Orbits in MATLAB
- Heteroclinic connections in plane Couette flow
- Approximation of box dimension of attractors using the subdivision algorithm
- Equilibrium and travelling-wave solutions of plane Couette flow
- Algorithms for Rigorous Entropy Bounds and Symbolic Dynamics
- On the Approximation of Complicated Dynamical Behavior
- Tertiary and quaternary solutions for plane Couette flow
- Transition in shear flows. Nonlinear normality versus non-normal linearity
- Detecting and Locating Near-Optimal Almost-Invariant Sets and Cycles
- Small scale exact coherent structures at large Reynolds numbers in plane Couette flow
- Deterministic Nonperiodic Flow
- Hydrodynamic Stability and Turbulence: Beyond Transients to a Self‐Sustaining Process
- Recipes for Continuation
- A Database Schema for the Analysis of Global Dynamics of Multiparameter Systems
- The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques
- TRANSPORT IN DYNAMICAL ASTRONOMY AND MULTIBODY PROBLEMS
- Efficient Automation of Index Pairs in Computational Conley Index Theory
- Turbulence transition in pipe flow: some open questions
- MATCONT
- Combinatorial Representation of Parameter Space for Switching Networks
- Periodic Orbits and Chaotic Sets in a Low-Dimensional Model for Shear Flows
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