Ginzburg--Landau Patterns in Circular and Spherical Geometries: Vortices, Spirals, and Attractors

DOI10.1137/20M1378739zbMath1483.35232arXiv1901.11496MaRDI QIDQ5860632

Phillipo Lappicy, Jia-Yuan Dai

Publication date: 22 November 2021

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

Full work available at URL: https://arxiv.org/abs/1901.11496

zbMATH Keywords

Ginzburg-Landau equationglobal attractorshyperbolicityspiral wavesshooting method\(m\)-armed vortex solutions

Mathematics Subject Classification ID

Attractors (35B41) Dynamical aspects of symmetries, equivariant bifurcation theory (37G40) Bifurcations in context of PDEs (35B32) Dynamical aspects of attractors and their bifurcations (37G35) Ginzburg-Landau equations (35Q56)

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Pattern-selective feedback stabilization of Ginzburg-Landau spiral waves

Cites Work

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• Steady-state bifurcation with O(3)-symmetry
• Rotating spiral waves in \(\lambda -\omega \) systems on circular domains
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Geometric theory of semilinear parabolic equations
• Target pattern and spiral solutions to reaction-diffusion equations with more than one space dimension
• Abstract forced symmetry breaking and forced frequency locking of modulated waves
• The mixed boundary condition for the Ginzburg Landau model in thin films
• Mathematical biology. Vol. 2: Spatial models and biomedical applications.
• Spiral wave behaviors in an excitable reaction-diffusion system on a sphere
• The symmetry perspective. From equilibrium to chaos in phase space and physical space
• On the stability of radial solutions of the Ginzburg-Landau equation
• Heteroclinic orbits of semilinear parabolic equations
• Instability of solutions to the Ginzburg-Landau equation on \(S^n\) and \(\mathbb{C} \mathbb{P}^n\)
• Bifurcations of topological type at singular points of parametrized vector fields
• Sturm attractors for quasilinear parabolic equations with singular coefficients
• Patterns and interfaces in dissipative dynamics. With a foreword by Y. Pomeau
• Partial differential equations. IX: Elliptic boundary value problems. Transl. from the Russian
• Instability of Ginzburg—Landau vortices on manifolds
• The world of the complex Ginzburg-Landau equation
• Spiral wave dynamics in excitable media with spherical geometries
• Generic properties of equilibria of reaction-diffusion equations with variable diffusion
• Spiral Waves for $\lambda -\omega $ Systems
• Analysis and Approximation of the Ginzburg–Landau Model of Superconductivity
• Bifurcation to Spiral Waves in Reaction-Diffusion Systems
• The stability of the radial solution to the ginzburg-landau equation
• Ginzburg--Landau Vortices: Dynamics, Pinning, and Hysteresis
• The chemical basis of morphogenesis
• Global Attractors for Parabolic Problems in Fractional Power Spaces
• Spiral Waves in Reaction-Diffusion Equations
• Some dynamical properties of Ginzburg-Landau vortices
• Ginzburg--Landau Spiral Waves in Circular and Spherical Geometries
• Period-Doubling of Spiral Waves and Defects
• Symmetric Spiral Patterns on Spheres
• On Second Order Differential Inequalities