  This paper addresses the problem of giving conditions for transcriptional
systems to be globally entrained to external periodic inputs. By using
contraction theory, a powerful tool from dynamical systems theory, it is shown
that certain systems driven by external periodic signals have the property that
all solutions converge to a fixed limit cycle. General results are proved, and
the properties are verified in the specific case of some models of
transcriptional systems. The basic mathematical results needed from contraction
theory are proved in the paper, making it self-contained.
