We have performed molecular-dynamics simulation to analyze structural phase transitions in a two-dimensional system using a model which has been proposed to study pressure-induced martensitic transformation in iron. At low temperatures, the square↔hexagonal phase transition was observed at P∗=5.4(1) and the reverse transition occurred only by application of tension on the system. At a temperature near the melting point, the hexagonal phase was reached at P∗=3.1(1) and it went back to square symmetry at P∗=1.9(1) showing hysteresis. The activation energy for this transition was evaluated using the nudged elastic band method. Our work permitted to detail the mechanism of square↔hexagonal transformations, contributing for a better understanding about the dynamics of self-organization phenomenon.