  We study both theoretically and experimentally switching dynamics in surface
stabilized ferroelectric liquid crystal cells with asymmetric boundary
conditions. In these cells the bounding surfaces are treated differently to
produce asymmetry in their anchoring properties. Our electro-optic measurements
of the switching voltage thresholds that are determined by the peaks of the
reversal polarization current reveal the frequency dependent shift of the
hysteresis loop. We examine the predictions of the uniform dynamical model with
the anchoring energy taken into account. It is found that the asymmetry effects
are dominated by the polar contribution to the anchoring energy. Frequency
dependence of the voltage thresholds is studied by analyzing the properties of
time-periodic solutions to the dynamical equation (cycles). For this purpose,
we apply the method that uses the parameterized half-period mappings for the
approximate model and relate the cycles to the fixed points of the composition
of two half-period mappings. The cycles are found to be unstable and can only
be formed when the driving frequency is lower than its critical value. The
polar anchoring parameter is estimated by making a comparison between the
results of modelling and the experimental data for the shift vs frequency
curve. For a double-well potential considered as a deformation of the
Rapini-Papoular potential, the branch of stable cycles emerges in the low
frequency region separated by the gap from the high frequency interval for
unstable cycles.
