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In this paper we investigate ghost dark energy model in the presence
of non-linear interaction between dark energy and dark matter. The functional form
of dark energy density in the generalized ghost dark
energy (GGDE) model is $\rho_D\equiv f(H, H^2)$ with
coefficient of $H^2$ represented by $\zeta$ and the model contains three free parameters as $\Omega_D, \zeta$ and $b^2$ (the coupling coefficient of interactions). We propose three kinds of non-linear interaction terms and discuss the behavior of equation of state,
deceleration and dark energy density parameters of the model. We also find the squared sound speed and search for signs of stability of the model.
To compare the interacting GGDE model with
observational data sets, we use more recent observational outcomes,
namely SNIa, gamma-ray bursts, baryonic acoustic oscillation
and the most relevant CMB parameters including, the position of
acoustic peaks, shift parameters and redshift to recombination. For GGDE
with the first non-linear interaction, the joint analysis
indicates that $\Omega_D=0.7009^{+0.0077}_{-0.0077}$,
$b^2=0.171^{+0.042}_{-0.042}$ and $\zeta=0.116^{+0.044}_{-0.098}$
at 1 optimal variance error. For the second interaction, the best fit
values at $1\sigma$ confidence are
$\Omega_D=0.6961^{+0.0084}_{-0.0084}$,
$b^2=0.054^{+0.011}_{-0.014}$ and $\zeta\le0.0445$. According to
combination of all observational data sets considered in this
paper the best fit values for third non-linearly interacting model are
$\Omega_D=0.6947^{+0.0086}_{-0.0086}$,
$b^2=0.0143^{+0.0032}_{-0.0054}$ and $\zeta\le0.0326$ at $1\sigma$
confidence interval. Finally we found that the presence of
interaction is confirmed in mentioned models via current
observational data sets.
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