Automatic Exploration Techniques of Numerical Bifurcation Diagrams Illustrated by the Ginzburg--Landau Equation

DOI10.1137/19M1248467zbMath1431.37066arXiv1903.02377MaRDI QIDQ5207549

Wim Vanroose, Michiel Wouters

Publication date: 3 January 2020

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.02377

zbMATH Keywords

superconductorsLyapunov-Schmidt reductionnumerical continuationGinzburg-Landau systemequivariant branching lemmaautomatic exploration

Mathematics Subject Classification ID

Computational methods for bifurcation problems in dynamical systems (37M20) Ginzburg-Landau equations (35Q56)

Related Items (max. 100)

Towards Scalable Automatic Exploration of Bifurcation Diagrams for Large-Scale Applications

Uses Software

• MATCONT
• AUTO
• LOCA
• KryPy
• PyNosh
• Python
• GitHub
• PyNCT

Cites Work

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• A Framework for Deflated and Augmented Krylov Subspace Methods
• Generalized Deflated Block-Elimination
• Pattern Formation
• Generation of Finite Difference Formulas on Arbitrarily Spaced Grids
• Stable Solvers and Block Elimination for Bordered Systems
• Analysis and Approximation of the Ginzburg–Landau Model of Superconductivity
• BIFURCATION TRACKING ALGORITHMS AND SOFTWARE FOR LARGE SCALE APPLICATIONS
• Solving General Auxin Transport Models with a Numerical Continuation Toolbox in Python: PyNCT
• Numerical Bifurcation Study of Superconducting Patterns on a Square
• MATCONT
• Bifurcation points and bifurcated branches by an asymptotic numerical method and Padé approximants

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