A STUDY ON THE EXISTENCE OF LIMIT CYCLES OF A PLANAR SYSTEM WITH THIRD-DEGREE POLYNOMIALS

DOI10.1142/S0218127404009247zbMath1078.34017MaRDI QIDQ4655561

Pei Yu, Yiping Lin, Mao'an Han

Publication date: 8 March 2005

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

zbMATH Keywords

centerlimit cyclenormal formplanar systemHilbert's 16th problemfocus value

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Perturbations of ordinary differential equations (34D10) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (25)

Bifurcations of limit cycles in a cubic system ⋮ LOCAL AND GLOBAL BIFURCATIONS TO LIMIT CYCLES IN A CLASS OF LIÉNARD EQUATION ⋮ The problem of general center-focus and bifurcation of limit cycles for a planar system of nine degrees ⋮ HOPF BIFURCATIONS FOR NEAR-HAMILTONIAN SYSTEMS ⋮ General center conditions and bifurcation of limit cycles for a quasi-symmetric seventh degree system ⋮ ON THE NUMBER AND DISTRIBUTION OF LIMIT CYCLES IN A CUBIC SYSTEM ⋮ Center, limit cycles and isochronous center of a \(Z_{4}\)-equivariant quintic system ⋮ Existence of limit cycles for a class of quartic polynomial differential system depending on parameters ⋮ Bifurcations of limit circles and center conditions for a class of non-analytic cubic \(Z_2\) polynomial differential systems ⋮ Small amplitude limit cycles and local bifurcation of critical periods for a quartic Kolmogorov system ⋮ Limit cycle bifurcations in a class of quintic \(Z_2\)-equivariant polynomial systems ⋮ BIFURCATION OF LIMIT CYCLES IN A FOURTH-ORDER NEAR-HAMILTONIAN SYSTEM ⋮ Complete study on a bi-center problem for the \(Z_2\)-equivariant cubic vector fields ⋮ Limit cycles in generalized Liénard systems ⋮ Limit cycles and invariant curves in a class of switching systems with degree four ⋮ On the bifurcation of double homoclinic loops of a cubic system ⋮ On limit cycles of the Liénard equation 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 ⋮ Thirteen limit cycles for a class of cubic Hamiltonian system with higher-order perturbed terms ⋮ HOPF BIFURCATION OF A THREE-DIMENSIONAL SYSTEM ⋮ TWELVE LIMIT CYCLES IN A CUBIC CASE OF THE 16th HILBERT PROBLEM ⋮ Limit cycles and isochronous centers in a class of ninth degree system ⋮ EIGHT LIMIT CYCLES AROUND A CENTER IN QUADRATIC HAMILTONIAN SYSTEM WITH THIRD-ORDER PERTURBATION ⋮ Limit Cycles in a Class of Quartic Kolmogorov Model with Three Positive Equilibrium Points

Uses Software

• Maple

Cites Work

• Vibration analysis on a thin plate with the aid of computation of normal forms
• Bifurcation set and limit cycles forming compound eyes in a perturbed Hamiltonian system
• Computing centre conditions for certain cubic systems
• Polynomial systems from certain differential equations
• COMPUTATION OF NORMAL FORMS VIA A PERTURBATION TECHNIQUE
• SYMBOLIC COMPUTATION OF NORMAL FORMS FOR RESONANT DOUBLE HOPF BIFURCATIONS USING A PERTURBATION TECHNIQUE
• On the conditions of Kukles for the existence of a Centre
• On the Paper of Jin and Wang Concerning the conditions for a Centre in certain Cubic Systems
• Degenerate Hopf Bifurcation Formulas and Hilbert’s 16th Problem

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