We propose a dynamical mechanism for the two-way switching between the metastable state and the stable state, which has been found in experiments of photoinduced reversible magnetization and photoinduced structural phase transitions. We find that the two-way switching by a nonsymmetry-breaking perturbation such as illumination is possible only in systems with appropriate parameters. We investigate the relaxation dynamics with two kinds of transition probabilities by a mean-field theory and a Monte Carlo method. We make it clear that the existence of two time scales in the dynamical process is important for the two-way switching and we actually demonstrate stable two-way switching.
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