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

DOI10.1007/s10114-010-6487-2zbMath1194.34074OpenAlexW2053380598MaRDI QIDQ966562

Yu-Hai Wu, Lixin Tian, Xuedi Wang

Publication date: 23 April 2010

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

Full work available at URL: https://doi.org/10.1007/s10114-010-6487-2

zbMATH Keywords

bifurcationlimit cycle\(Z_4\)-equivariant quintic planar vector field

Mathematics Subject Classification ID

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

On the number of limit cycles of a \(\mathbb{Z}_4\)-equivariant quintic near-Hamiltonian system ⋮ On the Number of Limit Cycles by Perturbing a Piecewise Smooth Liénard Model ⋮ On the 16th Hilbert problem for discontinuous piecewise polynomial Hamiltonian systems ⋮ Bifurcations of limit cycles in equivariant quintic planar vector fields ⋮ Limit cycles bifurcated from some \(Z_4\)-equivariant quintic near-Hamiltonian systems ⋮ 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 ⋮ Limit cycle bifurcations by perturbing a class of planar quintic vector fields ⋮ Symbolic computation for the qualitative theory of differential equations

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