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The dynamics of optically-injected semiconductor lasers are of great practical interest for various applications such as chaotic signal transmission. For the first time, a method is presented to obtain a complete picture of the dynamics for optically-injected systems simulated with the travelling-wave model by investigating their trajectories. The method uses the distribution of intersection points of the trajectory on a Poincare plane to distinguish between different dynamical states of the system. It is then applied to obtain stability maps for the reflected and transmitted light of three quarter-wave-shifted distributed-feedback lasers with different Bragg coupling coefficients and it is shown that, firstly, the dynamics are different for the reflected and transmitted light and, secondly, the locking bandwidth for the case with lower Bragg coupling coefficient is significantly increased. Both findings are in agreement with published results obtained by a different analysis. The obtained stability maps are then applied to find three points inside each locking region for which the longitudinal power and carrier distributions along the cavity are displayed. These distributions are compared with the solitary laser and the relation between the Bragg coupling coefficient and its influence on the shape of the power and carrier distributions is shown.