  We explore the consequences of incorporating parity and time reversal
($\mathcal{PT}$) symmetries on the dynamics of nonreciprocal light propagation
exhibited by a class of nonuniform periodic structures known as chirped
$\mathcal{PT}$-symmetric fiber Bragg gratings (FBGs). The interplay among
various grating parameters such as chirping, detuning, nonlinearities, and
gain/loss gives rise to unique bi- and multi-stable states in the unbroken as
well as broken $\mathcal{PT}$-symmetric regimes. The role of chirping on the
steering dynamics of the hysteresis curve is influenced by the type of
nonlinearities and the nature of detuning parameter. Also, incident directions
of the input light robustly impact the steering dynamics of bistable and
multistable states both in the unbroken and broken $\mathcal{PT}$-symmetric
regimes. When the light launching direction is reversed, critical stable states
are found to occur at very low intensities which opens up a new avenue for an
additional way of controlling light with light. We also analyze the phenomenon
of unidirectional wave transport and the reflective bi- and multi-stable
characteristics at the so-called $\mathcal{PT}$-symmetry breaking point.
