On the limit cycles of a quintic planar vector field

DOI10.1007/s11425-007-0045-0zbMath1136.34039OpenAlexW1573851763MaRDI QIDQ2461487

Lixin Tian, Yu-Hai Wu, Mao'an Han

Publication date: 28 November 2007

Published in: Science in China. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-007-0045-0

zbMATH Keywords

bifurcationdouble homoclinic loopquintic Hamiltonian systemseparate items Melnikov function

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) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (2)

Bifurcations of limit cycles in equivariant quintic planar vector fields ⋮ Bifurcations of limit cycles in a \(Z_{4}\)-equivariant quintic planar vector field

Cites Work

• Unnamed Item
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Bifurcation set and limit cycles forming compound eyes in a perturbed Hamiltonian system
• Cyclicity 1 and 2 conditions for a 2-polycycle of integrable systems on the plane
• Cyclicity of planar homoclinic loops and quadratic integrable systems
• Mathematical problems for the next century
• On the number of limit cycles in double homoclinic bifurcations
• Bifurcations of limit cycles for a cubic Hamiltonian system under quartic perturbations
• Bifurcation of limit cycles near polycycles with \(n\) vertices
• The stability of double homoclinic loops.
• A new cubic system having eleven limit cycles
• On the stability of double homoclinic and heteroclinic cycles.
• Bifurcations of limit cycles in a \(Z_6\)-equivariant planar vector field of degree 5
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• ON THE STUDY OF LIMIT CYCLES OF THE GENERALIZED RAYLEIGH–LIENARD OSCILLATOR

This page was built for publication: On the limit cycles of a quintic planar vector field