EXISTENCE CONDITIONS OF THIRTEEN LIMIT CYCLES IN A CUBIC SYSTEM

DOI10.1142/S0218127410027209zbMath1202.34065MaRDI QIDQ3065771

Pei Yu, Junmin Yang, Mao'an Han, Ji-Bin Li

Publication date: 6 January 2011

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

zbMATH Keywords

bifurcationlimit cyclepolynomial systemcubic

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)

Related Items (14)

Chemical systems with limit cycles ⋮ Center and isochronous center conditions for switching systems associated with elementary singular points ⋮ THE CENTER-FOCUS PROBLEM AND BIFURCATION OF LIMIT CYCLES IN A CLASS OF 7TH-DEGREE POLYNOMIAL SYSTEMS ⋮ Complex integrability and linearizability of cubic \(Z_2\)-equivariant systems with two \(1:q\) resonant singular points ⋮ SMALL LIMIT CYCLES BIFURCATING FROM Z₄-EQUIVARIANT NEAR-HAMILTONIAN SYSTEM OF DEGREES 9 AND 7 ⋮ Limit cycles and invariant curves in a class of switching systems with degree four ⋮ Complex isochronous centers and linearization transformations for cubic \(Z_2\)-equivariant planar systems ⋮ Integrability and linearizability of cubic \(Z_2\) systems with non-resonant singular points ⋮ EIGHT LIMIT CYCLES AROUND A CENTER IN QUADRATIC HAMILTONIAN SYSTEM WITH THIRD-ORDER PERTURBATION ⋮ The study on cyclicity of a class of cubic systems ⋮ On the Limit Cycles of a Perturbed Z₃-Equivariant Planar Quintic Vector Field ⋮ AN APPLICATION OF REGULAR CHAIN THEORY TO THE STUDY OF LIMIT CYCLES ⋮ Simultaneous integrability and non-linearizability at arbitrary double weak saddles and sole weak focus of a cubic Liénard system ⋮ The CD45 Case Revisited

Cites Work

• Unnamed Item
• Limit cycles near homoclinic and heteroclinic loops
• A cubic system with thirteen limit cycles
• Bifurcation set and limit cycles forming compound eyes in a perturbed Hamiltonian system
• On Hopf cyclicity of planar systems
• Twelve limit cycles in a cubic order planar system with \(Z_2\) symmetry
• Bifurcation of limit cycles near polycycles with \(n\) vertices
• Perturbation from an asymmetric cubic Hamiltonian
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• THE SAME DISTRIBUTION OF LIMIT CYCLES IN FIVE PERTURBED CUBIC HAMILTONIAN SYSTEMS
• TWELVE LIMIT CYCLES IN A CUBIC CASE OF THE 16th HILBERT PROBLEM
• On hereditarily indecomposable Banach spaces

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