Theorem: van der Pol (mu>0) has unique attracting limit cycle in R^2 via Poincare-Bendixson

Theorem (van der Pol unique-limit-cycle via Poincare-Bendixson): the 2D phase-space (x, y = dx/dt) of the van der Pol oscillator d^2x/dt^2 - mu*(1 - x^2)*dx/dt + x = 0 with mu > 0 admits a unique attracting limit cycle Gamma_mu. The…