Dynamics of nonminimally coupled scalar field models with generic potentials in FLRW background

We study the phase space analysis of a nonminimally coupled scalar field model with different potentials such as KKLT, Higgs, inverse and inverse square. Our investigation brings new asymptotic regimes, and obtains stable de-Sitter solution. In case of KKLT, we do not find stable de-Sitter solution whereas Higgs model satisfies the de-Sitter condition but does not provide a stable de-Sitter solution in usual sense as one of the eigenvalue is zero. We obtain time derivative of Hubble constant $\dot{H}=0$, equation of state $w_{\phi}\simeq -1$, scalar field $\phi=$constant and the positive effective gravitational constant ($G_{eff}>0$), which are missed in our earlier work. Therefore, in case of $F(\phi)R$ coupling with $F(\phi)= 1-\xi\phi^2$ and the models of inverse and inverse square potentials$-$ a true stable de-Sitter solution is trivially satisfied.