Bifurcation of limit cycles in a quintic Hamiltonian system under a sixth-order perturbation

DOI10.1016/j.chaos.2005.03.010zbMath1098.37057OpenAlexW2124951737MaRDI QIDQ2484761

Sharon Wang, Pei Yu

Publication date: 1 August 2005

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2005.03.010

zbMATH Keywords

perturbationlimit cyclesHopf bifurcationsHamiltonian systemnormal form theoryplanar polynomial systemslocal and global bifurcations

Mathematics Subject Classification ID

Normal forms for dynamical systems (37G05) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (33)

Bifurcations of limit cycles in a \(Z_6\)-equivariant planar vector field of degree 7 ⋮ AN IMPROVED LOWER BOUND ON THE NUMBER OF LIMIT CYCLES BIFURCATING FROM A QUINTIC HAMILTONIAN PLANAR VECTOR FIELD UNDER QUINTIC PERTURBATION ⋮ Bifurcation of small limit cycles in \(Z_{5}\)-equivariant planar vector fields of order 5 ⋮ Amplitude control of limit cycles in Langford system ⋮ Bifurcations of limit cycles for a perturbed quintic Hamiltonian system with four infinite singular points ⋮ On the number of limit cycles of a \(\mathbb{Z}_4\)-equivariant quintic near-Hamiltonian system ⋮ Bifurcation theory for finitely smooth planar autonomous differential systems ⋮ Periodic solutions for differential systems in \(\mathbb{R}^5\) and \(\mathbb{R}^6 \) ⋮ Hilbert's sixteenth problem for polynomial Liénard equations ⋮ On the 16th Hilbert problem for discontinuous piecewise polynomial Hamiltonian systems ⋮ Weak-foci of high order and cyclicity ⋮ Bifurcation of Limit Cycles in a 12-Degree Hamiltonian System Under Thirteenth-Order Perturbation ⋮ Bifurcations of limit cycles in equivariant quintic planar vector fields ⋮ Lower bounds for the Hilbert number of polynomial systems ⋮ Existence of 121 limit cycles in a perturbed planar polynomial Hamiltonian vector field of degree 11 ⋮ Bifurcations of limit cycles in a perturbed quintic Hamiltonian system with six double homoclinic loops ⋮ Novel frequency-domain criterion for elimination of limit cycles in a class of digital filters with single saturation nonlinearity ⋮ Modified LMI condition for the realization of limit cycle-free digital filters using saturation arithmetic ⋮ Limit cycle bifurcations in a class of near-Hamiltonian systems with multiple parameters ⋮ New lower bounds for the Hilbert numbers using reversible centers ⋮ The number and distributions of limit cycles for a class of quintic near-Hamiltonian systems ⋮ SMALL LIMIT CYCLES BIFURCATING FROM Z₄-EQUIVARIANT NEAR-HAMILTONIAN SYSTEM OF DEGREES 9 AND 7 ⋮ Suppression of limit cycles in second-order companion form digital filters with saturation arithmetic ⋮ Bifurcations of limit cycles in a \(Z_{4}\)-equivariant planar polynomial vector field of degree 7 ⋮ On limit cycles of the Liénard equation with \(Z_2\) symmetry ⋮ On some open problems in planar differential systems and Hilbert's 16th problem ⋮ Bifurcations of limit cycles in a \(Z_{4}\)-equivariant quintic planar vector field ⋮ AN IMPROVED LOWER BOUND ON THE NUMBER OF LIMIT CYCLES BIFURCATING FROM A HAMILTONIAN PLANAR VECTOR FIELD OF DEGREE 7 ⋮ On the perturbations of a Hamiltonian system ⋮ Detection function method and its application to a class of quintic Hamiltonian systems with quintic perturbations ⋮ On the limit cycles of a Hamiltonian under \(Z_4\)-equivariant quintic perturbation ⋮ Poincaré bifurcation of limit cycles from a Liénard system with a homoclinic loop passing through a nilpotent saddle ⋮ Symbolic computation for the qualitative theory of differential equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence of 121 limit cycles in a perturbed planar polynomial Hamiltonian vector field of degree 11
• Abelian integrals and bifurcation theory
• Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields
• Mathematical problems for the next century
• Bifurcations of limit cycles in a \(Z_8\)-equivariant planar vector field of degree 7
• Twelve limit cycles in a cubic order planar system with \(Z_2\) symmetry
• 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
• Bifurcations of limit cycles in a \(Z_6\)-equivariant planar vector field of degree 5
• COMPUTATION OF NORMAL FORMS VIA A PERTURBATION TECHNIQUE
• The number of limit cycles for a class of quintic Hamiltonian systems under quintic perturbations
• Degenerate homoclinic cycles in perturbations of quadratic Hamiltonian systems
• On the global analysis of the planar quadratic vector fields
• Essential Maple 7
• Centennial History of Hilbert's 16th Problem
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• ON THE CONTROL OF PARAMETERS OF DISTRIBUTIONS OF LIMIT CYCLES FOR A Z₂-EQUIVARIANT PERTURBED PLANAR HAMILTONIAN POLYNOMIAL VECTOR FIELD
• The Geometry of Quadratic Differential Systems with a Weak Focus of Third Order
• TWELVE LIMIT CYCLES IN A CUBIC CASE OF THE 16th HILBERT PROBLEM

This page was built for publication: Bifurcation of limit cycles in a quintic Hamiltonian system under a sixth-order perturbation