Hopf bifurcation with \(D_ 3\times D_ 3\)-symmetry

DOI10.1007/BF00948479zbMath0782.34041OpenAlexW2914768962MaRDI QIDQ687414

Michael Wegelin, Gerhard Dangelmayr, Werner Güttinger

Publication date: 24 October 1993

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00948479

zbMATH Keywords

symmetryperiodic solutionsnormal formisotropy subgroupshierarchical structurequasiperiodic solutionsheteroclinic cyclesgeneric Hopf bifurcationthree interacting sets of three oscillators

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (4)

Hopf bifurcations in three coupled oscillators with internal symmetries ⋮ Complex dynamics near a Hopf bifurcation with symmetry: A parameter study ⋮ Multiple nonlinear oscillations in a \(\mathbb D_3\times\mathbb D_3\)-symmetrical coupled system of identical cells with delays ⋮ Synchronized patterns in hierarchical networks of neuronal oscillators with \({\mathbb{D}}_3\times{\mathbb{D}}_3\) symmetry

Cites Work

• Unnamed Item
• Singularities and groups in bifurcation theory. Volume II
• Symmetry-breaking Hopf bifurcation in anisotropic systems
• Hopf bifurcation with the symmetry of the square
• Hopf-steady-state mode interactions with 0(2) symmetry
• Hopf bifurcation on a square lattice
• Asymptotic stability of heteroclinic cycles in systems with symmetry. II
• Hopf bifurcation in the presence of symmetry

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