Localizing attractors via a generalized La Salle principle
We are concerned with plane differential systems of the form (x)over dot = P(x,y), (y)over dot = 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 partial derivativeV/partial derivativex + Q partial derivativeV/partial derivativey = mu(V), with mu is an arbitrary analytic function. When mu(V) = rho(V -V-2), rho > 0, the attractors are contained in the set V = 1, the repellers in the set V = 0. (C) 2002 Elsevier Science Ltd. All rights reserved.
limit cycles liapunov functions polynomial systems computer algebra rayleigh equation