Bifurcation of limit cycles at the equator for a class of polynomial differential system

DOI10.1016/j.nonrwa.2007.11.021zbMath1167.37341OpenAlexW2000220296MaRDI QIDQ837692

Gui Weihua, Qi Zhang, Yi-rong Liu

Publication date: 20 August 2009

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2007.11.021

zbMATH Keywords

infinitybifurcation of limit cyclepolynomial system of degree sevensingular point quantity

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

Related Items (4)

Bifurcation of limit cycles at degenerate singular point and infinity in a septic system ⋮ The multiplicity of the equatorial limit cycle of a class of planar polynomial 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

Uses Software

• Mathematica

Cites Work

• Bifurcation at infinity in polynomial vector fields
• Bifurcations of limit cycles from infinity for a class of quintic polynomial system
• Stability and bifurcations of limit cycles of the equator in a class of cubic polynomial systems.
• A polynomial differential system with nine limit cycles at infinity
• A cubic polynomial system with seven limit cycles at infinity
• A quintic polynomial differential system with eleven limit cycles at the infinity
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