  An algorithm is presented here, for discovering Hopf-Bifurcation varieties of
polynomial dynamical systems. It is based on the expression of specific
polynomials, as sums of products of first degree polynomials, with parametrical
coefficients. By giving to these parameters certain values, we ensure the
positiveness of some quantities, constructing thereby proper Lyapunov
functions, which guarantee the stability of the equilibrium point. The points
where the afore mentioned positiveness fails, define the Hopf-Bifurcation
varieties upon discussion.
