Phase transition in a harmonic oscillator with dynamical traps

We consider the characteristic features of a new class of nonequilibrium phase transitions, namely, transitions due to dynamical traps. We studied an individual oscillator with dynamical traps located in a small neighborhood of the x axis of the phase plane {x, v = dx/dt}. The dynamics of this system is analyzed numerically. The mechanism and conditions of the occurrence of various dynamic states is established. We demonstrate that the dynamics of such an oscillator can be represented by a number of random jump-like transitions between long-lived states. For these states to occur, random forces are necessary with intensity lying within a certain interval. If the intensity of the random forces is high or low, phase transitions due to dynamical traps will not occur.