  We reduce a one-dimensional model of an active segment (AS), which is used,
for instance, in the description of contraction driven cell motility on tracks,
to a zero-dimensional model of an active particle (AP) characterized by two
internal degrees of freedom: position and polarity. Both models give rise to
hysteretic force-velocity relations showing that an active agent can support
two opposite polarities under the same external force and that it can maintain
the same polarity while being dragged by external forces with opposite
orientations. This double bi-stability results in a rich dynamic repertoire
which we illustrate by studying static, stalled, motile and periodically
re-polarizing regimes displayed by an active agent confined in a visco-elastic
environment. We show that the AS and AP models can be calibrated to generate
quantitatively similar dynamic responses.
