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Recently \citet{PEDE:2019ApJ} proposed a phenomenologically emergent darkenergy (PEDE) which consider that the dark energy density evolves as$\widetilde{\Omega}_{\rm{DE}}(z)\,=\,\Omega_{\rm{DE,0}}\left[ 1 -{\rm{tanh}}\left( {\log}_{10}(1+z) \right) \right]$ with the advantage that itdoes not have degree of freedom. Later on, \citet{PEDE:2020} proposed ageneralized model by adding one degree of freedom to the PEDE model, encoded inthe parameter $\Delta$. Motivated by these proposals, we constrain theparameter space ($h,\Omega_m$) and ($h,\Omega_m, \Delta$) for PEDE andGeneralized Emergent Dark Energy (GEDE) respectively, by employing the mostrecent observational (non-) homogeneous Hubble data. Additionally, wereconstruct the deceleration and jerk parameters and estimate yield values at$z=0$ of $q_0 = -0.784^{+0.028}_{-0.027}$ and $j_0 = 1.241^{+0.164}_{-0.149}$for PEDE and $q_0 = -0.730^{+0.059}_{-0.067}$ and $j_0 =1.293^{+0.194}_{-0.187}$ for GEDE using the homogeneous sample. We reportvalues on the deceleration-acceleration transition redshift with those reportedin the literature within $2\sigma$ CL. Furthermore, we perform a stabilityanalysis of the PEDE and GEDE models to study the global evolution of theUniverse around their critical points. Although the PEDE and GEDE dynamics aresimilar to the standard model, our stability analysis indicates that in bothmodels there is an accelerated phase at early epochs of the Universe.

Generalized Emergent Dark Energy: observational Hubble data constraints and stability analysis