Bifurcations of limit cycles from infinity for a class of quintic polynomial system. (English) Zbl 1070.34064

The paper is devoted to a class of quintic systems. By means of special transformations infinity is mapped turn into the origin. Having found the relation between focal values and singular point values, the authors investigate bifurcations of limit cycles of the original system from infinity. In such way, a quintic system with a small parameter and eight other parameters can be constructed, where 8 limit cycles can bifurcate from infinity.


34C23 Bifurcation theory for ordinary differential equations
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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