A hexagonal two-dimensional model of particles with displacive degrees of freedom and interacting via potential energy with harmonic and anharmonic third- and fourth-order terms has been studied by the molecular-dynamics technique. The modulated phases characterized by the wave vectors lying in the interval from 1/4 to 1/3 have been specifically considered. The simulations have shown that: (i) the 1q commensurate 1/4 --> 1/3 1q incommensurate phase transition is driven by the stripple mechanism. The stripples are built from four discommensuration planes and the serial mechanism of stripple correlated nucleation has been observed. (ii) The reverse phase transition from 1q incommensurate to 1q commensurate 1/4 phase was obtained only under extreme metastable conditions. No antistripples with four discommensurations were observed. Instead, a rearrangement of same domains gave a possibility to remove discommensuration planes by simple antistripples built up from two discommensurations only. (iii) At the 3q --> 1q phase transition, the columns of 3q phase merged together to form a stripe of a 1q incommensurate phase. (iv) The commensurate phase 1/3 is degenerate with respect to the 1q and 3q modulation patterns. [References: 24]