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We focus on the dynamical feature for a $p$-wave superconductor model in different parameter regions in terms of the appearance of gapless edge modes in reel geometry. Firstly, we show the parameter region with gapless edge modes versus a parameter and quasi-momentum. The parameter diagram can be reflected by the expectations of Pauli matrices in global manners. In another view, the dynamical feature of the excitation behave differently in the parameter regions with topological gapless edge modes and not. And the cusps of dynamical return rate vanish as the parameter pass the boundary in the parameter region slowly enough. It is found that the dynamics in the parameter region with gapless edge modes behaves differently to that without edge modes and related mostly to the eigenenergy gap between the pre-and post-quench eigenstates. The cusps of the dynamical return rate behave robustly against the noise in the lattice until localization behavior dominates. This work benefits detecting topological edge modes by dynamical manners.