First part: background and and basic methods The analytical problem of nding Hopf bifurcation xed points for polynomial or rational vector elds (or determining that there are none) can be reduced to a purely semi-algebraic question. In the rst part of the talk we explore this possibility by rst giving a reduction of the parametric question on the existence of a Hopf bifurcation xed point to a parametric rst-order formula over the ordered elds of the real. We show the results of solving these with existing tools from computational logic (such as Redlog ) for several standard and text book examples and compare the results of these fully automated methods to the ones of hand analyses given in textbooks.