  In this work we shall study the late-time dynamics of several $F(R)$ gravity
models. By appropriately expressing the field equations in terms of the
redshift and of a statefinder function, we shall solve numerically the field
equations using appropriate physical motivated initial conditions. We consider
models which, by construction, are described by a nearly $R^2$-model at early
epochs and we fine tune the parameters to achieve viability and compatibility
with the latest Planck constraints at late times. Such models provide a unified
description of inflation and dark energy era and notably a common feature of
all the models is the presence of dark energy oscillations. Furthermore, we
show that, in contrast to general relativistic fluids and scalar field
descriptions, a large spectrum of different dark energy physics is generated by
simple $F(R)$ gravity models, varying from phantom, to nearly de Sitter and to
quintessential dark energy eras.
