N-body simulations have shown that a bar in a galaxy can be triggered by two processes: (1) by its own instabilities in the disk, or (2) by interactions with other galaxies. Both mechanisms have been widely studied. However, the literature has not shown measurements of the critical limits of the disk stability parameters (DSPs). We show measurements of those parameters through the whole evolution in isolated disk models and find that the initial rotation configuration of those models stays in the stable or unstable regime from the initial to the final evolution. Then we perturbed the isolated models to study the evolution of DSPs under perturbation. We find that the critical limits of DSPs are not much affected in barred models, but when the bar is triggered by a perturbation, the disk falls into the unstable regimen. We show in our models that a bar triggered by a light perturbation grows in two phases: first, the bar appears as a slow rotator, and then it evolves to be a fast rotator; second, when the perturbation is far from the target galaxy, the bar evolves from fast to slow rotator. When the bar is triggered by a heavy perturbation, it appears as a fast rotator and evolves to be a slow rotator, similar to classical bar models.