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

DOI10.1016/j.matcom.2011.05.001zbMath1242.34050OpenAlexW2037142161MaRDI QIDQ654351

Feng Li, Hong-Wei Li, Yi-rong Liu

Publication date: 28 December 2011

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2011.05.001

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) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Software, source code, etc. for problems pertaining to ordinary differential equations (34-04)

Related Items (8)

Two kinds of bifurcation phenomena in a quartic system ⋮ Bi-center problem and bifurcation of limit cycles from nilpotent singular points in \(Z_{2}\)-equivariant cubic vector fields ⋮ Limit cycles and integrability in a class of systems with high-order nilpotent critical points ⋮ Limit cycles and integrability in a class of system with a high-order critical point ⋮ Limit cycles in a quartic system with a third-order nilpotent singular point ⋮ Center conditions for nilpotent cubic systems using the Cherkas method ⋮ Center-focus and Hopf bifurcation for a class of quartic Kukles-like systems ⋮ Fourteen limit cycles in a seven-degree nilpotent system

Uses Software

• Mathematica

Cites Work

• Unnamed Item
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• Singularities of vector fields
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• The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems
• 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
• 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

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