Five limit cycles for a simple cubic system
The authors consider a system \[ x'=\lambda x+y+Ax^2+Bxy, y'=-x+\lambda y+Kx^2+Lxy+My^2+Nx^3. \] They reduce it to a Liénard-type system to find new necessary conditions for the origin to be a center. It is shown that the origin is a fine focus of maximal order five, and the corresponding Lyapunov quantities are explicitly found. It follows that a system of the considered type can have five limit cycles.
scientific article; zbMATH DE number 1057642