ON THE NUMBER AND DISTRIBUTIONS OF LIMIT CYCLES IN A QUINTIC PLANAR VECTOR FIELD

DOI10.1142/S0218127408021464zbMath1149.34318OpenAlexW2043228698MaRDI QIDQ3544968

Yong-Xi Gao, Wu Yuhai, Mao'an Han

Publication date: 8 December 2008

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

Full work available at URL: https://doi.org/10.1142/s0218127408021464

zbMATH Keywords

stabilitylimit cyclesbifurcationMelnikov functiondouble homoclinic loopsdistributions of limit cycles

Mathematics Subject Classification ID

Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (11)

On the number of limit cycles of a \(\mathbb{Z}_4\)-equivariant quintic near-Hamiltonian system ⋮ Hilbert's sixteenth problem for polynomial Liénard equations ⋮ Extended quasi-homogeneous polynomial system in \({\mathbb{R}^{3}}\) ⋮ Bifurcations of limit cycles in equivariant quintic planar vector fields ⋮ Lower bounds for the Hilbert number of polynomial systems ⋮ New lower bounds for the Hilbert numbers using reversible centers ⋮ SMALL LIMIT CYCLES BIFURCATING FROM Z₄-EQUIVARIANT NEAR-HAMILTONIAN SYSTEM OF DEGREES 9 AND 7 ⋮ Bifurcations of limit cycles in a \(Z_{4}\)-equivariant quintic planar vector field ⋮ On the perturbations of a Hamiltonian system ⋮ Complex isochronous centers and linearization transformations for cubic \(Z_2\)-equivariant planar systems ⋮ On the Limit Cycles of a Perturbed Z₃-Equivariant Planar Quintic Vector Field

Cites Work

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• Bifurcations of limit cycles in a cubic system
• BIFURCATION OF LIMIT CYCLES IN A FOURTH-ORDER NEAR-HAMILTONIAN SYSTEM
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• ON THE STUDY OF LIMIT CYCLES OF THE GENERALIZED RAYLEIGH–LIENARD OSCILLATOR
• TWELVE LIMIT CYCLES IN A CUBIC CASE OF THE 16th HILBERT PROBLEM

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