STABILITY COMPUTATIONS FOR NILPOTENT HOPF BIFURCATIONS IN COUPLED CELL SYSTEMS

DOI10.1142/S0218127407018658zbMath1141.37343OpenAlexW2118742026MaRDI QIDQ3511072

Martin Krupa, Martin Golubitsky

Publication date: 4 July 2008

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127407018658

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Dynamics induced by flows and semiflows (37C10) Dynamical aspects of symmetries, equivariant bifurcation theory (37G40) Stability of manifolds of solutions to ordinary differential equations (34D35)

Related Items (9)

Normal Forms for Codimension One Planar Piecewise Smooth Vector Fields ⋮ Center Manifolds of Coupled Cell Networks ⋮ Projection blocks in homogeneous coupled cell networks ⋮ Center Manifolds of Coupled Cell Networks ⋮ Normal resonances in a double Hopf bifurcation ⋮ Circulant type formulas for the eigenvalues of linear network maps ⋮ The Pauli exclusion principle. Can it be proved? ⋮ Graph fibrations and symmetries of network dynamics ⋮ Coupled cell networks: Semigroups, Lie algebras and normal forms

Cites Work

• A simple global characterization for normal forms of singular vector fields
• Hopf bifurcation with non-semisimple 1:1 resonance
• Symmetry Groupoids and Patterns of Synchrony in Coupled Cell Networks
• Patterns of Synchrony in Coupled Cell Networks with Multiple Arrows
• Nilpotent Hopf Bifurcations in Coupled Cell Systems

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