Center problem and the bifurcation of limit cycles for a cubic polynomial system

DOI10.1016/j.apm.2015.03.037zbMath1443.34028OpenAlexW2001296105MaRDI QIDQ2282401

Chao-xiong Du, Qi Zhang, Wen-tao Huang

Publication date: 7 January 2020

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apm.2015.03.037

zbMATH Keywords

bifurcationlimit cyclefocal valuesimultaneous center

Mathematics Subject Classification ID

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)

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Isochronicity for a \(Z_{2}\)-equivariant cubic system ⋮ Liénard Equation and Its Generalizations ⋮ LIMIT CYCLE BIFURCATION FOR A NILPOTENT SYSTEM IN <i>Z</i>₃-EQUIVARIANT VECTOR FIELD ⋮ Double bifurcation for a cubic Kolmogorov model ⋮ Behavior of limit cycle bifurcations for a class of quartic Kolmogorov models in a symmetrical vector field

Cites Work

• Center-focus problem and limit cycles bifurcations for a class of cubic Kolmogorov model
• The bifurcation of limit cycles in \(Z_n\)-equivariant vector fields
• New results on the study of \(Z_q\)-equivariant planar polynomial vector fields
• On the 16th Hilbert problem for limit cycles on nonsingular algebraic curves
• Theory of values of singular point in complex autonomous differential systems
• Small limit cycles bifurcating from fine focus points in cubic order \(Z_{2}\)-equivariant vector fields
• The problem of general center-focus and bifurcation of limit cycles for a planar system of nine degrees
• General center conditions and bifurcation of limit cycles for a quasi-symmetric seventh degree system
• Three-Dimensional Hopf Bifurcation for a Class of Cubic Kolmogorov Model
• Limit Cycles Bifurcations for a Class of Kolmogorov Model in Symmetrical Vector Field
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS

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