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Recently, a Friedmann-Robertson-Walker universe filled with variouscosmological fluids has been considered by S.D. Odintsov et al. in [30] fromphase space vantage point where various expressions for the Equation-of-State(EoS) parameter were studied. Since these types of EoS parameters aregenerative of appreciable results in the Hilbert-Einstein model, hence weintend to investigate all the cases in a homogeneous $F(T)$-gravity ($T$ is thetorsion) through phase space analysis in precise detail. In short, three viablemodels of interaction between dark matter and dark energy, includingusual-type, power-law type, and oscillating type, are investigatedcomprehensively. It is indicated that the power-law interaction in the relateddynamical systems should be of increasing nature with time to get more criticalpoints. Due to the failure of the oscillating model of ref. [30] in$F(T)$-gravity, four modified models are suggested and examined in both $F(T)$and Hilbert-Einstein models. As to be seen, the modified models not only aregenerative of critical points equivalent to that of ref. [30], but also giverise to further critical points covering crucial stages of the evolution of theuniverse. In the context of these four models, such as the old one, at earlytimes the interactions are negligible and they commence to grow as the cosmictime approaches the late-time in which the unification of early inflation andlate acceleration is obtained. Using an indirect method, it is shown that theoscillating models have substantial roles in transitions between eras.

Phase space of multi-fluid universe in $F(T)$-gravity and some enhancements for the oscillating interaction model