SMALL LIMIT CYCLES BIFURCATING FROM Z4-EQUIVARIANT NEAR-HAMILTONIAN SYSTEM OF DEGREES 9 AND 7

DOI10.1142/S0218127412502720zbMath1258.34061OpenAlexW2072882724MaRDI QIDQ4908377

Junmin Yang, Xian Bo Sun

Publication date: 5 March 2013

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

Full work available at URL: https://doi.org/10.1142/s0218127412502720

zbMATH Keywords

Hopf bifurcationnear-Hamiltonian system\(Z_4\)-equivariancesmall limit cycle

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) Dynamical aspects of symmetries, equivariant bifurcation theory (37G40)

Related Items (3)

Simultaneity of centres in ℤ _q -equivariant systems ⋮ Bifurcation of limit cycles from a Liénard system with a heteroclinic loop connecting two nilpotent saddles ⋮ The number of small amplitude limit cycles in arbitrary polynomial systems

Cites Work

• Bifurcation of small limit cycles in \(Z_{5}\)-equivariant planar vector fields of order 5
• Existence of 121 limit cycles in a perturbed planar polynomial Hamiltonian vector field of degree 11
• Bifurcations of limit cycles in a \(Z_{4}\)-equivariant quintic planar vector field
• A cubic system with thirteen limit cycles
• On Hopf cyclicity of planar systems
• Small limit cycles bifurcating from fine focus points in quartic order \(Z_{3}\)-equivariant vector fields
• A cubic system with twelve small amplitude limit cycles
• Bifurcation of limit cycles in a quintic Hamiltonian system under a sixth-order perturbation
• EXISTENCE CONDITIONS OF THIRTEEN LIMIT CYCLES IN A CUBIC SYSTEM
• ON THE NUMBER AND DISTRIBUTIONS OF LIMIT CYCLES IN A QUINTIC PLANAR VECTOR FIELD
• BIFURCATION OF LIMIT CYCLES IN Z₁₀-EQUIVARIANT VECTOR FIELDS OF DEGREE 9
• HOPF BIFURCATIONS FOR NEAR-HAMILTONIAN SYSTEMS
• BIFURCATIONS OF LIMIT CYCLES IN A Z₂-EQUIVARIANT PLANAR POLYNOMIAL VECTOR FIELD OF DEGREE 7

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