taken to be the same as above figures. The influence coming from the interaction $\alpha$ and equation of state of dark energy $w_X$ can be seen clearly in this figure. We notice that a positive $\alpha$ makes the redshift of acceleration/deceleration transition ($q(z_T)=0$) shift to a smaller value; while the values of $z_T$ are nearly degenerate under the same $\alpha$ as shown in this example.

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Statefinder diagnostic
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Since more and more dark energy models have been constructed for interpreting or describing the cosmic acceleration, the problem of discriminating between the various contenders becomes very important. In order to be able to differentiate between those competing cosmological scenarios involving dark energy, a sensitive and robust diagnostic for dark energy models is a must. For this purpose a diagnostic proposal that makes use of parameter pair $\{r,s\}$, the so-called “statefinder”, was introduced by Sahni et al. [@sahni]. The statefinder probes the expansion dynamics of the Universe through higher derivatives of the scale factor $\stackrel{...}{a}$ and is a natural companion to the deceleration parameter $q$ which depends upon $\ddot a$. The statefinder pair $\{r,s\}$ is defined as follows $$r\equiv
\frac{\stackrel{...}{a}}{aH^3},~~~~s\equiv\frac{r-1}{3(q-1/2)}~.\label{rs}$$ The statefinder is a “geometrical” diagnostic in the sense that 