Limit cycles and isochronous centers in a class of ninth degree system. (English) Zbl 1470.34086

Hongwei, Li; Feng, Li; Chaoxiong, Du

Abstr. Appl. Anal. 2013, Article ID 762751, 8 p. (2013).

Summary: A class of ninth degree system is studied and the conditions ensuring that its five singular points can be centers and isochronous centers (or linearizable centers) at the same time by exact calculation and strict proof are obtained. What is more, the expressions of Lyapunov constants and periodic constants are simplified, and 21 limit circles could be bifurcated at least.

MSC:

34C05	Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C07	Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations

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