The third-order analytical solution of dynamic power system is used to investigate the complex nonlinear dynamical behavior of power systems after the occurrence of large disturbances. A new point of view is presented firstly to theoretically explain the reason of the increasing amplitude inertia mode oscillations after occurring large disturbances， that the higher order terms in the third-order analytical solutions are exited by the large disturbance and the nonlinear interaction among the modes is intensified. The analysis result for a power system case shows that the new finding is correct and the third-order analytical solution is more effective in analyzing the complex dynamical behavior of power systems after occurring large disturbances than the second-order analytical solution.