Analysis on limit cycles of \(Z_{q}\)-equivariant polynomial vector fields with degree 3 or 4
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Publication:2497381
DOI10.1016/j.jmaa.2005.08.068zbMath1106.34017OpenAlexW2103282672MaRDI QIDQ2497381
Publication date: 4 August 2006
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jmaa.2005.08.068
limit cyclenormal formnumerical simulationHilbert's 16th problem\(Z_{q}\)-equivariant polynomial vector field
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Related Items (14)
Bi-center problem and bifurcation of limit cycles from nilpotent singular points in \(Z_{2}\)-equivariant cubic vector fields ⋮ Center, limit cycles and isochronous center of a \(Z_{4}\)-equivariant quintic system ⋮ Bifurcations of limit circles and center conditions for a class of non-analytic cubic \(Z_2\) polynomial differential systems ⋮ Limit Cycles for a Class of Zp-Equivariant Differential Systems ⋮ Limit cycle bifurcations in a class of quintic \(Z_2\)-equivariant polynomial systems ⋮ A Quartic System with Twenty-Six Limit Cycles ⋮ Bifurcations of limit cycles in a \(Z_{4}\)-equivariant planar polynomial vector field of degree 7 ⋮ The number of small amplitude limit cycles in arbitrary polynomial systems ⋮ On the number of limit cycles of a \(Z_{4}\)-equivariant quintic polynomial system ⋮ Limit cycles for cubic systems with a symmetry of order 4 and without infinite critical points ⋮ Detection function method and its application to a class of quintic Hamiltonian systems with quintic perturbations ⋮ Thirteen limit cycles for a class of cubic Hamiltonian system with higher-order perturbed terms ⋮ Limit cycles of a \(Z_3\)-equivariant near-Hamiltonian system ⋮ Limit cycles for 3-monomial differential equations
Cites Work
- Bifurcation set and limit cycles forming compound eyes in a perturbed Hamiltonian system
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- Mathematical problems for the next century
- Bifurcations of limit cycles for a cubic Hamiltonian system under quartic perturbations
- Small limit cycles bifurcating from fine focus points in cubic order \(Z_{2}\)-equivariant vector fields
- COMPUTATION OF NORMAL FORMS VIA A PERTURBATION TECHNIQUE
- HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
- TWELVE LIMIT CYCLES IN A CUBIC CASE OF THE 16th HILBERT PROBLEM
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