On the configurations of centers of planar Hamiltonian Kolmogorov cubic polynomial differential systems
This paper proposes a study of centers and their configurations for Hamiltonian cubic polynomial differential systems having two intersecting invariant straight lines. By applying an affine transformation these two invariant straight lines go through the axes of coordinates and these systems become Kolmogorov systems. The authors find that the real algebraic curve \(xy(a+bx+cy+dx^2+exy+fy^2)=h\) has at most four families of level ovals in the phase plane of such systems for all real parameters \(a\), \(b\), \(c\), \(d\), \(e\), \(f\) and \(h\).
scientific article; zbMATH DE number 7229711
scientific article