Bifurcation of a class of planar non-Hamiltonian integrable systems with one center and one homoclinic loop (Q1604602)

The Hilbert 16th problem is still open even for quadratic Hamiltonian systems with quadratic perturbations. Under some conditions, the authors establish bifurcation results for the following system \[ x'=-y +a x^2 +b y^2 +\delta(\nu_1 x+ \nu_2 x y), \qquad y'=x(1+ c y) +\delta \nu_3 x^2, \] with the numerical parameters \(a,b,c, \delta, \nu_k\), \(k=1,2,3\).