The global structural stability and application of the toroidal differntial equations\left\{ {\begin{array}{*{20}c} {\dot x = a_1 [\sin (x - y) - \sin x] - \Delta \omega } \\ {\dot y = a_2 [\sin (y - x) - \sin y] - \Delta \omega } \\ \end{array} } \right.

In this paper, the global structural stability of the toroidal differential equationshas been obtained, and applied to the cross-coupled phase - locked loop, where Δω≥0