Center conditions and bifurcation of limit cycles at three-order nilpotent critical point in a seventh degree Lyapunov system

DOI10.1016/j.cnsns.2010.06.017zbMath1221.34079OpenAlexW2002002014MaRDI QIDQ718580

Feng Li, Yusen Wu, Yi-rong Liu

Publication date: 23 September 2011

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2010.06.017

zbMATH Keywords

bifurcation of limit cyclesquasi-Lyapunov constantcenter-focus problemthree-order nilpotent critical point

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) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (5)

Multiple limit cycles bifurcation from the degenerate singularity for a class of three-dimensional systems ⋮ Existence and uniqueness of the exponentially stable limit cycle for a class of nonlinear systems via time-domain approach with differential inequality ⋮ LIMIT CYCLE BIFURCATION FOR A NILPOTENT SYSTEM IN <i>Z</i>₃-EQUIVARIANT VECTOR FIELD ⋮ Fourteen limit cycles in a seven-degree nilpotent system ⋮ The center conditions and bifurcation of limit cycles at the degenerate singularity of a three-dimensional system

Uses Software

• Mathematica

Cites Work

• On the structure of Poincaré-Lyapunov constants for the weak focus of polynomial vector fields
• Integrability of centers perturbed by quasi-homogeneous polynomials
• The analytic and formal normal form for the nilpotent singularity
• The center-focus problem for a system with homogeneous nonlinearities in the case of zero eigenvalues of the linear part
• Singularities of vector fields
• A new algorithm for the computation of the Lyapunov constants for some degenerated critical points.
• Generating limit cycles from a nilpotent critical point via normal forms
• Investigation of the behaviour of the integral curves of a system of two differential equations in the neighbourhood of a singular point
• Local analytic integrability for nilpotent centers
• Degenerate Hopf Bifurcation Formulas and Hilbert’s 16th Problem
• Symétrie et forme normale des centres et foyers dégénérés
• MONODROMY AND STABILITY FOR NILPOTENT CRITICAL POINTS
• Unnamed Item

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