written as (here ): The above proposition 2 tells that one must have: Because 1 > 0 and −1 < 0 are obvious, one can conclude that a Hopf bifurcation may occur for Van der Pol oscillator if . See also Reaction–diffusion systems References Further reading External links The Hopf Bifurcation Andronov–Hopf bifurcation page at Scholarpedia Bifurcation theory Circuit theorems