Melnikov's method and codimension-two bifurcations in forced oscillations

DOI10.1006/jdeq.2002.4177zbMath1027.34048OpenAlexW2042948719MaRDI QIDQ1864623

Kazuyuki Yagasaki

Publication date: 18 March 2003

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.2002.4177

zbMATH Keywords

Melnikov methodsubharmonic orbitBogdanov-Takens bifurcationhomoclinic tangencyforced oscillator

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

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Uses Software

• AUTO
• Dynamics
• HomCont

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• On nonconservative periodic systems close to two-dimensional Hamiltonian
• Numerical Detection and Continuation of Homoclinic Points and Their Bifurcations for Maps and Periodically Forced Systems
• Invariant circles in the Bogdanov-Takens bifurcation for diffeomorphisms
• The Melnikov Theory for Subharmonics and Their Bifurcations in Forced Oscillations
• Averaging methods in nonlinear dynamical systems
• Elements of applied bifurcation theory
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