  In this paper we study new cosmological models involving new forms of
non-gravitational interaction between cold dark matter and dark energy. The
main purpose is to demonstrate the applicability of the forms of interaction to
the problem in modern cosmology known as accelerated expansion of the large
scale universe. It is well known, that a non-gravitational interaction can
improve theoretical prediction, but a fundamental theory allowing to derive the
form of the interaction is missing. Therefore, an active sought to find a
correct form of the interaction from various phenomenological assumptions is
still one of the active branches of research in modern cosmology. Besides
cosmographic analysis, we perform $Om$ analysis.
