The present work analyzes the characteristics of bifurcations that arise in an equi-triangular arrangement of three stationary Rankine vortex filaments. The distances between the vortices are taken large enough so that effect of core deformation is negligible and the possibility of vortex merger does not arise. Kinematics of a fluid particle under the influence of vortex field has been formulated as a nonlinear dynamical system. The dynamical system possesses equilibrium points (EPs) that are "saddles" or "centers" with their number and location dependent on the relative strengths of the vortices. A change in the number of EPs is caused mainly by appearance or coalescence (merger) of the center and saddle pair. Initially, the two-vortex system has been investigated analytically to obtain the nature of EPs and resulting bifurcations and then the effect of a third vortex is investigated by varying its strength. Particle paths and interesting loci patterns for the EPs are observed and reported. Merger of two individual saddles into a double saddle is also observed in some cases. For various strength combinations and the same sense of rotation, all EPs lie inside the triangle formed by joining the centers of the vortices. However, for all the cases, the centers appear inside the vortex cores and saddles appear outside the vortex cores. © 2019 Begell House, Inc.