Bifurcations of limit cycles in a reversible quadratic system with a center, a saddle and two nodes
Consider the system \[ \dot{x}=-y-3x^{2}+by^{2},\quad\dot{y}=x(1-2y), \] where \(b\) is a real parameter. The exact upper bound for the number of limit cycles produced by the period annulus of the system under quadratic perturbations is called the cyclicity of the period annulus. By using the properties of related complete elliptic integrals and the geometry of some plane curves, the authors prove that, if \(b \geq 2\), \(b\neq 3\), then the cyclicity of the period annulus is two. This bound is exact.
scientific article; zbMATH DE number 5713045