ON THE CONTROL OF PARAMETERS OF DISTRIBUTIONS OF LIMIT CYCLES FOR A Z2-EQUIVARIANT PERTURBED PLANAR HAMILTONIAN POLYNOMIAL VECTOR FIELD

DOI10.1142/S0218127405012065zbMath1077.34037MaRDI QIDQ4675692

Hongxian Zhou, Ji-Bin Li

Publication date: 6 May 2005

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

zbMATH Keywords

limit cycleHopf bifurcationdetection functionHilbert's 16th problemsaddle-connection 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) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (11)

On the number of limit cycles of a cubic polynomials Hamiltonian system under quintic perturbation ⋮ Bifurcation of small limit cycles in \(Z_{5}\)-equivariant planar vector fields of order 5 ⋮ Bifurcations of limit cycles for a perturbed quintic Hamiltonian system with four infinite singular points ⋮ New results on the study of \(Z_q\)-equivariant planar polynomial vector fields ⋮ Bifurcation set and number of limit cycles in \(Z_{2}\)-equivariant planar vector fields of degree 5 ⋮ BIFURCATION OF MULTIPLE LIMIT CYCLES FOR A ROTOR-ACTIVE MAGNETIC BEARINGS SYSTEM WITH TIME-VARYING STIFFNESS ⋮ \(Z_{2}\)-equivariant cubic system which yields 13 limit cycles ⋮ The number and distributions of limit cycles for a class of quintic near-Hamiltonian systems ⋮ Analysis on bifurcations of multiple limit cycles for a parametrically and externally excited mechanical system ⋮ Bifurcation of limit cycles in a quintic Hamiltonian system under a sixth-order perturbation ⋮ Detection function method and its application to a class of quintic Hamiltonian systems with quintic perturbations

Cites Work

• Bifurcation set and limit cycles forming compound eyes in a perturbed Hamiltonian system
• The number of limit cycles for a class of quintic Hamiltonian systems under quintic perturbations
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• INVESTIGATIONS OF BIFURCATIONS OF LIMIT CYCLES IN Z₂-EQUIVARIANT PLANAR VECTOR FIELDS OF DEGREE 5
• BIFURCATIONS OF LIMIT CYCLES IN A Z₃-EQUIVARIANT VECTOR FIELD OF DEGREE 5

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