Scenario of inflationary cosmology from the phenomenological $Lambda$ models

Choosing the three phenomenological models of the dynamical cosmological term $Lambda$, viz., $Lambda sim (dot a/a)^2$, $Lambda sim {ddot a/a}$ and $Lambda sim rho$ where $a$ is the cosmic scale factor, it has been shown by the method of numerical analysis that the three models are equivalent for the flat Universe $k=0$. The evolution plots for dynamical cosmological term $Lambda$ vs. time $t$ and also the cosmic scale factor $a$ vs. $t$ are drawn here for $k=0, +1$. A qualitative analysis has been made from the plots which supports the idea of inflation and hence expanding Universe.