  Cells and tissues exhibit oscillatory deformations during remodelling,
migration or embryogenesis. Although it has been shown that these oscillations
correlate with cell biochemical signalling, it is yet unclear the role of these
oscillations in triggering drastic cell reorganisation events or instabilities,
and the coupling of this oscillatory response with tested visco-elastic
properties.
  We here present a rheological model that incorporates elastic, viscous and
frictional components, and that is able to generate oscillatory response
through a delay adaptive process of the rest-length. We analyse its stability
properties as a function of the model parameters and deduce analytical bounds
of the stable domain. While increasing values of the delay and remodelling rate
render the model unstable, we also show that increasing friction with the
substrate destabilise the oscillatory response. Furthermore, we numerically
verify that the extension of the model to non-linear strain measures is able to
generate sustained oscillations that alternate between stable and unstable
regions.
