Bifurcations of a cubic system perturbed by degree five

DOI10.1016/S0252-9602(09)60002-3zbMath1199.34165MaRDI QIDQ846818

Tonghua Zhang, Desheng Shang

Publication date: 12 February 2010

Published in: Acta Mathematica Scientia. Series B. (English Edition) (Search for Journal in Brave)

zbMATH Keywords

perturbationlimit cyclehomoclinic loopsingular point value

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) Perturbations of ordinary differential equations (34D10) 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) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

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Bifurcations in a Cubic System with a Degenerate Saddle Point ⋮ The monotonicity of the ratio of two Abelian integrals

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