The advance in single-cell profiling technologies and the development in computational algorithms provide the opportunity to reconstruct pseudo temporal trajectory with branch point of cellular development. On the other hand, theories such as dynamical network biomarkers (DNB) theory have been recently proposed to characterize the pre-transition state in biological systems. Few studies have validated whether the branch point identified in pseudo time is the critical point in dynamical system. In this study, the dynamical behavior of the branch point on the pseudo trajectory has been investigated. We study the pseudo temporal trajectories reconstructed by Wishbone and diffusion pseudotime analysis (DPT) algorithms, as well as the simulated trajectory. DNB theory is applied to justify the bifurcating event on the pseudo trajectories. Our results demonstrate that the branch point recovered by Wishbone and DPT algorithms is confirmed as a transition state in cell differentiation process by DNB theory. Furthermore, we show that an appropriate DNB group will amplify the comprehensive index of critical event as defined in DNB theory. Our study provides biological insights on pseudo trajectory with branch point in a dynamical view and also indicates that DNB theory may serve as a benchmark to check the validity of branch point.