Complex dynamics in the Hopf bifurcation with broken translation symmetry

DOI10.1016/0167-2789(95)00227-8zbMath0891.34044OpenAlexW1972136277MaRDI QIDQ1905727

P. Hirschberg, Edgar Knoblauch

Publication date: 16 January 1996

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

Full work available at URL: https://doi.org/10.1016/0167-2789(95)00227-8

zbMATH Keywords

coupled complex Ginzburg-Landau equations\(O(2)\)-equivariant Hopf bifurcationgluing bifurcationssmall amplitude complex behavior

Mathematics Subject Classification ID

Related Items (7)

Complex dynamics near a Hopf bifurcation with symmetry: A parameter study ⋮ Partial classification of heteroclinic behaviour associated with the perturbation of hexagonal planforms ⋮ Bursts in oscillatory systems with broken \(D_4\) symmetry ⋮ Global bifurcations in the Takens-Bogdanov normal form with \(D_4\) symmetry near the \(O(2)\) limit ⋮ Wrinkled tori and bursts due to resonant temporal forcing ⋮ Pinning and locking of discrete waves ⋮ INTERMITTENCY AND CHAOS NEAR HOPF BIFURCATION WITH BROKEN 𝕆(2) × 𝕆(2) SYMMETRY

Cites Work

• Bifurcations in a model of magnetoconvection
• Local and global behavior near homoclinic orbits
• Global bifurcations and chaos. Analytical methods
• One dimensional spatial structure near a Hopf bifurcation at finite wavenumber
• Singularities and groups in bifurcation theory. Volume II
• Shilnikov-Hopf bifurcation
• Mean flow suppression by endwalls in oscillatory binary fluid convection
• Merging of resonance tongues
• Hopf bifurcation with broken circular symmetry
• Transitions to chaos in two-dimensional double-diffusive convection
• A perturbed Hopf bifurcation with reflection symmetry
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