Localizing attractors via a generalized La Salle principle

We are concerned with plane differential systems of the formẋ = P(x,y), ẏ = Q(x,y), withP, Q analytic. We propose a formal-numeric method to localize the attractors and the repellers of the system. Such a method consists of looking for a power series solution to a PDE of the typeP∂V∂x + Q∂V∂y = μ(V), with μ is an arbitrary analytic function. Whenμ(V) = ρ(V − V2),ρ > 0, the attractors are contained in the setV = 1, the repellers in the setV = 0.