Bifurcation sequences in the interaction of resonances in a model deriving from nonlinear rotordynamics: The zipper

DOI10.1080/713603734zbMath0955.34029OpenAlexW2131341602MaRDI QIDQ4500168

G. H. M. Van Der Heijden

Publication date: 27 February 2001

Published in: Dynamics and Stability of Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/713603734

zbMATH Keywords

bifurcationTakens-Bogdanov bifurcationzippernonlinear rotordynamicstranscritical bifurcationsresonant periodic orbitschaotic Šil'nikov bifurcationsparameterized four-dimensional autonomous system

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Complex behavior and chaotic systems of ordinary differential equations (34C28) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (4)

Complex oscillations and waves of calcium in pancreatic acinar cells ⋮ Dynamics in the 1:2 spatial resonance with broken reflection symmetry ⋮ New type of complex dynamics in the \(1:2\) spatial resonance ⋮ Regular and chaotic dynamics of a discontinuously nonlinear rotor system.

Uses Software

• AUTO

Cites Work

• Unnamed Item
• Three coupled oscillators: Mode-locking, global bifurcations and toroidal chaos
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Transition to topological chaos for circle maps
• Bifurcations from an invariant circle for two-parameter families of maps of the plane: a computer-assisted study
• Merging of resonance tongues
• The non-transverse Shil'nikov-Hopf bifurcation: uncoupling of homoclinic orbits and homoclinic tangencies
• Quantitative universality for a class of nonlinear transformations
• Mode-locking in nonlinear rotordynamics
• Successive homoclinic tangencies to a limit cycle
• Repeated Resonance and Homoclinic Bifurcation in a Periodically Forced Family of Oscillators
• NUMERICAL DETECTION AND CONTINUATION OF CODIMENSION-TWO HOMOCLINIC BIFURCATIONS
• NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (I): BIFURCATION IN FINITE DIMENSIONS

This page was built for publication: Bifurcation sequences in the interaction of resonances in a model deriving from nonlinear rotordynamics: The zipper