In this work we focus on defining how dynamism can be modeled in the context of multi-objective optimization. Based on this, we construct a component oriented classification for dynamic multi-objective optimization problems. For each category we provide synthetic examples that depict in a more explicit way the defined model. We do this either by positioning existing synthetic benchmarks with respect to the proposed classification or through new problem formulations. In addition, an online dynamic MNK-landscape formulation is introduced together with a new comparative metric for the online dynamic multi-objective context.