An index to evaluate the influence on oscillation behavior of both nonlinearity and time-variance is proposed. The absolute value of the index is zero for a steady linear model， and increases with the nonlinearity and time variation factors of the model. Therefore， effects of the different factors can be compared quantitatively. Since the disturbed trajectories fully reflect the effects on dynamic behaviors of these factors including time-delay and discrete actions， the wavelet ridge algorithm is used to analyze oscillation modes within a proper time window along the trajectories. Then a time series of oscillation modes are obtained with sliding the window. This can be used to quantitatively assess time-varying nonlinear oscillations and restrain strong oscillations. Simulations on a 3-machine 9-node system show that the dynamic behaviors may be fully different from eigenvalue results at the equilibrium point， and the latter may even miss the most critical nonlinear modes.