Hopf bifurcation at the nonzero foci in 1∶4 resonance

DOI10.1007/BF02108858zbMath0724.34045OpenAlexW2317100642MaRDI QIDQ5758504

Duo Wang

Publication date: 1990

Published in: Acta Mathematica Sinica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02108858

zbMATH Keywords

Hopf bifurcationdifferential equationcomplex1:4 resonance

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Ordinary differential equations in the complex domain (34M99) Nonlinear resonances for nonlinear problems in mechanics (70K30)

Related Items

The Bifurcation Set for the 1:4 Resonance Problem, HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Classification and unfoldings of degenerate Hopf bifurcations
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• Integral averaging and bifurcation
• Bifurcation into invariant tori at points of resonance
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