×

zbMATH — the first resource for mathematics

Bifurcations of limit cycles of a quadratic system with two singular points and two parameters turning the field. (Russian) Zbl 0643.34035
Nonlinear differential equations in the plane with quadratic vector fields are investigated. Under the additional condition that the only fixed points are a focus (at the origin) and a saddle the general form of such a system is given, being linear equivalent to any other system with this property. Two parameters are then inroduced such that for varying one of them always a limit cycle with a special property exists. If both parameters are changed along a simple curve then bifurcations to two or three limit cycles may occur. Conditions are given where even four limit cycles can coexist. Some examples are derived and solved numerically.
Reviewer: G.Jetschke

MSC:
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
PDF BibTeX XML Cite