  Window functions are widely employed in memristor models to restrict the
changes of the internal state variables to specified intervals. Here we show
that the actual choice of window function is of significant importance for the
predictive modelling of memristors. Using a recently formulated theory of
memristor attractors, we demonstrate that whether stable fixed points exist
depends on the type of window function used in the model. Our main findings are
formulated in terms of two memristor attractor theorems, which apply to broad
classes of memristor models. As an example of our findings, we predict the
existence of stable fixed points in Biolek window function memristors and their
absence in memristors described by the Joglekar window function, when such
memristors are driven by periodic alternating polarity pulses. It is
anticipated that the results of this study will contribute toward the
development of more sophisticated models of memristive devices and systems.
