  In this paper, we investigate the mathematical modeling for the cosmological
attractors propagated in mimetic gravity upon which an interacting dark
energy-dark matter is supposed to be existed. The average value of the
interaction of these percentages, namely $\Gamma_i$ say, may be used to
investigate generally the modeling of an attractor; the actual value could only
be determined by data in any particular case. We have seen, for example, that
it was led to investigate the subject of initially invariant submanifolds.
