  In this research, we are interested in constraining the nonlinear interacting
and noninteracting Tsallis holographic dark energy (THDE) with Ricci horizon
cutoff by employing three observational datasets. To this aim, the THDE with
Ricci horizon considering the noninteraction and nonlinear interaction terms
will be fitted by the SNe Ia, SNe Ia+H(z), and SNe Ia+H(z)+GRB samples to
investigate the Hubble ($H(z)$), dark energy equation of state ($\omega_{DE}$),
effective equation of state ($\omega_{eff}$), and deceleration ($q$)
parameters. Investigating the $H(z)$ parameter illustrates that our models are
in good consistent with respect to observation. Also, it can reveal the turning
point for both noninteracting and nonlinear interacting THDE with Ricci cutoff
in the late time era. Next, the analysis of the $\omega_{DE}$ for our models
displays that the dark energy can experience the phantom state at the current
time. However, it lies in the quintessence regime in the early era and
approaches the cosmological constant in the late-time epoch. Similar results
will be for the $\omega_{eff}$ parameter with this difference that the
$\omega_{eff}$ will experience the quintessence region at the current redshift.
Next to the mentioned parameters, the study of the $q$ parameter indicates that
the models satisfy an acceptable transition phase from the matter to the dark
energy-dominated era. After that, the classical stability ($v_{s}^{2}$) will be
analyzed for our models. The $v_{s}^{2}$ shows that the noninteracting and
nonlinear interacting THDE with Ricci cutoff will be stable in the past era,
unstable in the present, and progressive epochs. Then, we will employ the
$Jerk$ ($J$) and $OM$ parameters to distinguish between our models and the
$\Lambda CDM$ model. Finally, we will calculate the age of the Universe for the
THDE and nonlinear interacting THDE with Ricci as the IR cutoff.
