A dynamical system d X/d t = F(X; A) is treated where F(X; A) is a polynomial (or some general type of radical contained) function in the vectors of state variables X ϵ ℝ ⁿ and parameters A ϵ ℝ ^m. We are looking for stability domains in both spaces, i.e. (a) domain ℙ ⊂ ℝ ^m such that for any parameter vector specialization A ϵ ℙ, there exists a stable equilibrium for the dynamical system, and (b) domain ⊂ ℝ ⁿ such that any point X _∗ ϵ could be made a stable equilibrium by a suitable specialization of the parameter vector A.