Bifurcation of limit cycles and the cusp of ordern

DOI10.1007/BF02560525zbMath0890.34032MaRDI QIDQ4358832

Mao'an Han

Publication date: 9 June 1998

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

zbMATH Keywords

limit cyclesbifurcationcenterunfolding

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Bifurcation theory for ordinary differential equations (34C23) Local and nonlocal bifurcation theory for dynamical systems (37G99)

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Abelian Integrals from an Unfolding of Codimension-3 Singularities with Nilpotent Linear Part ⋮ Bogdanov-Takens bifurcation in predator-prey systems ⋮ Abelian integrals in unfoldings of codimension 3 singularities with nilpotent linear parts ⋮ HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS ⋮ Existence of at most 1, 2, or 3 zeros of a Melnikov function and limit cycles ⋮ On Hopf cyclicity of planar systems with multiple parameters ⋮ On Uniqueness of Limit Cycles in General Bogdanov–Takens Bifurcation ⋮ On Hopf cyclicity of planar systems

Cites Work

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• The cusp of order n
• Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3
• On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
• Generalized Hopf Bifurcation and Its Dual Generalized Homoclinic Bifurcation