Algebraic and Radical Potential Fields. Stability Domains in Coordinate and Parametric Space

摘要

A dynamical system dX/dt= 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 ∈ R~n and parameters A ∈ 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 ∈ R~m. there exists a stable equilibrium for the dynamical system, and (b) domain S ? R~n such that any point X_* ∈ S could be made a stable equilibrium by a suitable specialization of the parameter vector A.