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Some bifurcation diagrams for limit cycles of quadratic differential systems. (English) Zbl 1090.37558

Summary: Concrete numerical examples of quadratic differential systems having three limit cycles surrounding one singular point are shown. In case another finite singular point also exists, a (3, 1) distribution of limit cycles is also obtained. This is the highest number of limit cycles known to occur in a quadratic differential system so far. Representative bifurcation diagrams are drawn for realistic parameter values.

MSC:

37M20 Computational methods for bifurcation problems in dynamical systems
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
65P30 Numerical bifurcation problems
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