On cosmology of interacting varying polytropic dark fluids

In this paper a possibility of the accelerated expansion of the large scale universe with a varying polytropic fluid of a certain type is presented. About a special role of non-gravitational interactions between dark energy and dark matter, in particular, about a possibility of improvement and solution of problems arising in modern cosmology, has been discussed for a long time. This motivates us to consider new models, where non-gravitational interactions between varying polytropic fluid and cold dark matter are allowed. Mainly non-linear interactions of a specific type is considered, found in recent literature. In order to understand the behavior of suggested cosmological models, besides cosmographic analysis, $Om$ analysis is applied. Moreover, with different datasets, including a strong gravitational lensing dataset, the observational constraints on the model parameters are obtained using $\chi^{2}$ analysis.