Takens-Bogdanov bifurcation on the hexagonal lattice for double-layer convection

DOI10.1016/S0167-2789(99)00007-XzbMath0948.76021OpenAlexW2165003600WikidataQ127663663 ScholiaQ127663663MaRDI QIDQ1808275

Kaoru Fujimura, Michael Renardy, Yuriko Yamamuro Renardy

Publication date: 6 December 1999

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

Full work available at URL: https://doi.org/10.1016/s0167-2789(99)00007-x

zbMATH Keywords

periodic solutionsquasiperiodic solutionsamplitude equationschaotic regimeBénard problemheteroclinic solutionshexagonal latticesecondary bifurcationsTakens-Bogdanov bifurcationstwo-fluid layers

Mathematics Subject Classification ID

Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Stratification effects in viscous fluids (76D50) Convection in hydrodynamic stability (76E06)

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Cites Work

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• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Bifurcating solutions at the onset of convection in the Bénard problem for two fluids
• Fundamentals of two-fluid dynamics. Part I: Mathematical theory and applications
• Singularities and groups in bifurcation theory. Volume II
• The Fuller index and global Hopf bifurcation
• The 2:1 steady/Hopf mode interaction in the two-layer Bénard problem
• Hopf bifurcation on the hexagonal lattice with small frequency
• Pattern formation for oscillatory bulk-mode competition in a two-layer Bénard problem
• Bifurcation on the hexagonal lattice and the planar Bénard problem
• The Takens-Bogdanov bifurcation with O(2)-symmetry
• A theoretical and experimental study of double-layer convection
• Time-periodic thermal convection in Hele–Shaw slots: The diagonal oscillation
• Global Bifurcations of Periodic Orbits
• Strong spatial interactions with 1:1 resonance: a three-layer convection problem
• On the Hopf bifurcation occurring in the two-layer Rayleigh–Bénard convective instability