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Metamorphoses of phase portraits of vector field in the case of symmetry of order 4

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Publication:1183237
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DOI10.1016/0022-0396(92)90045-OzbMath0753.34023MaRDI QIDQ1183237

Yi-Sui Sun, Chong-Qing Cheng

Publication date: 28 June 1992

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


zbMATH Keywords

symmetrynormal form theoryHopf bifurcations with periodic forcingnon autonomous systems


Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Ordinary differential equations in the complex domain (34M99)


Related Items

The Bifurcation Set for the 1:4 Resonance Problem, Limit cycles for cubic systems with a symmetry of order 4 and without infinite critical points, Limit cycles for 3-monomial differential equations



Cites Work

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  • Example of a quadratic system with two cycles appearing in a homoclinic loop bifurcation
  • Hopf bifurcations in nonautonomous systems at points of resonance
  • Bifurcation into invariant tori at points of resonance
  • A system with three limit cycles appearing in a Hopf bifurcation and dying in a homoclinic bifurcation: The cusp of order 4
  • Bifurcation of Critical Periods for Plane Vector Fields
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