Algebraic and radical potential fields. Stability domains in coordinate and parametric space.

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