Fourteen limit cycles in a seven-degree nilpotent system

DOI10.1155/2013/398609zbMath1298.34062OpenAlexW2144244312WikidataQ58916170 ScholiaQ58916170MaRDI QIDQ2015500

Ting Chen, Tianlong Gu, Wen-tao Huang

Publication date: 23 June 2014

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2013/398609

zbMATH Keywords

computer algebra systemcenter conditionsbifurcation of limit cycles\texttt{Mathematica}

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)

Uses Software

• Mathematica

Cites Work

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• Center conditions and bifurcation of limit cycles at three-order nilpotent critical point in a septic Lyapunov system
• Center conditions and bifurcation of limit cycles at three-order nilpotent critical point in a seventh degree Lyapunov system
• Local bifurcation of limit cycles and integrability of a class of nilpotent systems of differential equations
• The center-focus problem for a system with homogeneous nonlinearities in the case of zero eigenvalues of the linear part
• Limit cycle bifurcations from a nilpotent focus or center of planar systems
• Generating limit cycles from a nilpotent critical point via normal forms
• BIFURCATIONS OF LIMIT CYCLES AND CENTER PROBLEM FOR A CLASS OF CUBIC NILPOTENT SYSTEM
• ON THIRD-ORDER NILPOTENT CRITICAL POINTS: INTEGRAL FACTOR METHOD
• Investigation of the behaviour of the integral curves of a system of two differential equations in the neighbourhood of a singular point
• NEW STUDY ON THE CENTER PROBLEM AND BIFURCATIONS OF LIMIT CYCLES FOR THE LYAPUNOV SYSTEM (II)
• NEW STUDY ON THE CENTER PROBLEM AND BIFURCATIONS OF LIMIT CYCLES FOR THE LYAPUNOV SYSTEM (I)
• MONODROMY AND STABILITY FOR NILPOTENT CRITICAL POINTS

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