Global behavior of limit cycles in rotated vector fields
Consider a one-parameter family of vector fields \((*) \;dx/dt =f(x,\lambda)\) where \(f:D\times I \rightarrow \mathbb{R}^2\) is analytic, \(D\) is a connected set of \(\mathbb{R}^2, I\) is an interval. The author gives a definition of rotated vector fields which generalizes the definition given by \textit{L. Perko} [J. Differ. Equations 103, 127-145 (1993; Zbl 0781.34020)]. He studies the global behavior of limit cycles in dependence on \(\lambda\) such as nonintersection, persistence, bifurcation, and limit behavior. The results show that the well-known properties of rotated vector fields remain true under the relaxed definition.
scientific article; zbMATH DE number 1271363
scientific article