We investigate an interacting two-fluid model in a spatially flat
Friedmann-Lema\^itre-Robertson-Walker (FLRW) Universe, when the energy transfer
between these two dark components is produced by a factorisable nonlinear
sign-changeable interaction depending linearly on the energy density and
quadratically on the deceleration parameter. We solve the source equation and
obtain the effective energy densities of the dark sector and their components.
We show that the effective equation of state of the dark sector includes some
of the several kind of Chaplygin gas equations of state as well as a
generalization of the polytropic equation of state. We use bayesian statistics
methods to constrain free parameters in the models during its most recent
evolution considering supernovae type Ia and measurements of the Hubble
expansion rate. The resulting constraints provide new information on
sign-changeable interactions, its equivalences and compatibility with previous
models and novel late time universe dynamics.Comment: 8 figure
