We use an analytical gravitational model that describes the local motion of stars near the central region of a barred galaxy. By integrating and classifying large sets of starting conditions of trajectories we manage to determine how the important parameters of the bar, such as its mass, strength, scale length, and angular velocity influence the motion of stars. For the orbit taxonomy, we combine traditional dynamical methods such as the classical Poincare surface of section along with modern chaos indicators such as the Smaller Alignment Index (SALI). Our results of the local galactic model are compared with previous studies using global gravitational models.