 Furthermore, the claim is that study of such chaotic models can give us understanding of the behavior in corresponding actual-world systems. Not because the model trajectories are isomorphic to the system trajectories; rather, because there is a topological or geometric similarity or correspondence between the models and the systems being modeled. This is a different version of the faithful model assumption in that now the topological/geometric features of target systems are taken to be faithfully represented by our chaotic models. 