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Bifurcation of limit cycles in a particular class of quadratic systems. (English) Zbl 0815.34023

Authors’ abstract: “Within the class of quadratic perturbations we show analytically or numerically how many limit cycles can be bifurcated at first order out of the periodic orbits surrounding the center of the quadratic system \(\dot x=x(1-x-ay)\) and \(\dot y=y(-1+ax+y)\), where \(1<a<\infty\)”.

MSC:

34C23 Bifurcation theory for ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations