On Uniqueness of Limit Cycles in General Bogdanov–Takens Bifurcation

DOI10.1142/S0218127418501158zbMath1401.34045OpenAlexW2892242951MaRDI QIDQ4691114

Jaume Llibre, Junmin Yang, Mao'an Han

Publication date: 18 October 2018

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127418501158

zbMATH Keywords

limit cycleBogdanov-Takens bifurcation

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

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Cites Work

• Hopf and homoclinic bifurcations for near-Hamiltonian systems
• Limit cycles near homoclinic and heteroclinic loops
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Elements of applied bifurcation theory.
• On Hopf cyclicity of planar systems
• Theory of rotated equations and applications to a population model
• Bifurcation theory for finitely smooth planar autonomous differential systems
• Bifurcation of periodic orbits by perturbing high-dimensional piecewise smooth integrable systems
• The number of limit cycles of polynomial deformations of a Hamiltonian vector field
• 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
• Bifurcation of limit cycles and the cusp of ordern
• On the Number of Periodic Solutions of Delay Differential Equations
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• ON THE MAXIMUM NUMBER OF PERIODIC SOLUTIONS OF PIECEWISE SMOOTH PERIODIC EQUATIONS BY AVERAGE METHOD
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