Localizing attractors via a generalized La Salle principle

Abstract

Listen

Translate article

We are concerned with plane differential systems of the form x ̇ = P(x,y), y ̇ = Q(x,y) , with P, 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 type P ∂V ∂x + Q ∂V ∂y = μ(V) , with μ is an arbitrary analytic function. When μ( V) = ρ( V − V 2), ρ > 0, the attractors are contained in the set V = 1, the repellers in the set V = 0.