Olech theorem

In dynamical systems theory, the Olech theorem establishes sufficient conditions for global asymptotic stability of a two-equation system of non-linear differential equations. The result was established by Czesław Olech in 1963, based on joint work with Philip Hartman.
Theorem.
The differential equations formula_1, formula_2, where formula_3, for which formula_4 is an equilibrium point, is uniformly globally asymptotically stable if: