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We consider a fluid described by a parameterized EoS of the general form$P=(\gamma-1)\rho+p_{0}+\omega_{H}H+\omega_{H2}H^{2}+\omega_{dH}\dot{H}$\cite{Ren}, where $p_{0}$, $\omega_{H}$, $\omega_{H2}$ and $\omega_{dH}$ arefree parameters of the model, interacting with a Tachyonic field with arelativistic Lagrangian$L_{TF}=-V(\phi)\sqrt{1-\partial_{i}\phi\partial^{i}\phi}$. The acceleration ofthe Universe described by a scale factor $a(t)=t^{n}, (n>1)$. Underconsideration of different forms of interaction the field $\phi$ and thepotential $V(\phi)$ are recovered and graphical analysis performed. Forillustration purposes we fixed values of parameters of the models to provide $V\rightarrow 0$ for later stages of evolution, when $t \rightarrow \infty$.

A Matter with an effective EoS interacting with a tachynic field in an accelerating Universe