The Bifurcation Set for the 1:4 Resonance Problem

DOI10.1080/10586458.1994.10504283zbMath0828.34027OpenAlexW1979506444MaRDI QIDQ4842377

Bernd Krauskopf

Publication date: 2 January 1996

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/225398

zbMATH Keywords

bifurcation setversal unfolding\(\mathbb{Z}_ 4\)-equivariant planar vector field1:4 resonance problem

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Bifurcation theory for ordinary differential equations (34C23) Structural stability and analogous concepts of solutions to ordinary differential equations (34D30)

Related Items (4)

On local and global aspects of the 1:4 resonance in the conservative cubic Hénon maps ⋮ Resonance Phenomena in a Scalar Delay Differential Equation with Two State-Dependent Delays ⋮ Phase Portraits of Planar Vector Fields: Computer Proofs ⋮ Transport and bifurcation in a non-area-preserving two-dimensional map with applications to the discharge of pollution in an estuarine flow

Uses Software

• AUTO-86
• DSTool
• Unnamed Item

Cites Work

• Homoclinic bifurcation at resonant eigenvalues
• Applications of centre manifold theory
• Metamorphoses of phase portraits of vector field in the case of symmetry of order 4
• Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields
• The Saddle-Node Separatrix-Loop Bifurcation
• Bifurcation sequences at 1:4 resonance: an inventory
• Hopf bifurcation at the nonzero foci in 1∶4 resonance

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