A three-level model of spatial and temporal dynamic chaos induced by transitions from a quantum description of continuous medium motion to the classical limit is suggested. The basic microscopic level is formed by bundles of the Feynman trajectories corresponding to motion of individual quantum particles in the medium. The mesoscopic level forms differential distributions generated by a macroscopic drift of the basic trajectories. The macroscopic level itself is described by the phenomenological balance equations brought to a level of phase fibering of the mesoscopic model. An example of finding quantum trajectories is considered, and a general method of constructing induced mesostructures is described.