Local bifurcation of limit cycles and center problem for a class of quintic nilpotent systems

DOI10.1186/1687-1847-2012-45zbMath1291.34069OpenAlexW2169536835WikidataQ59270762 ScholiaQ59270762MaRDI QIDQ2448012

Yusen Wu, Luju Liu, Feng Li

Publication date: 29 April 2014

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-1847-2012-45

zbMATH Keywords

center problembifurcation of limit cyclesquasi-Lyapunov constantquintic nilpotent system

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 singular points in dynamical systems (37G10) 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 (4)

Existence of solutions for functional boundary value problems at resonance on the half-line ⋮ Solvability for nonlocal boundary value problems on a half line with \(\dim(\ker\, L)=2\) ⋮ On quasi-periodic solutions to a higher-order Emden-Fowler type differential equation ⋮ Solvability of integral boundary value problems at resonance in \(\mathbb R^n\)

Cites Work

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• Center conditions and bifurcation of limit cycles at three-order nilpotent critical point in a cubic Lyapunov system
• Cyclicity versus center problem
• On the structure of Poincaré-Lyapunov constants for the weak focus of polynomial vector fields
• Reversibility and classification of nilpotent centers
• 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
• Generating limit cycles from a nilpotent critical point via normal forms
• The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems
• Stability of motion
• BIFURCATIONS OF LIMIT CYCLES AND CENTER PROBLEM FOR A CLASS OF CUBIC NILPOTENT SYSTEM
• 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
• On the Poincaré–Lyapunov constants and the Poincare series
• 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
• The center-focus problem and reversibility

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