  The study on the collective dynamics of synchronization among genetic
oscillators is essential for the understanding of the rhythmic phenomena of
living organisms at both molecular and cellular levels. Genetic oscillators are
biochemical networks, which can generally be modelled as nonlinear dynamic
systems. We show in this paper that many genetic oscillators can be transformed
into Lur'e form by exploiting the special structure of biological systems. By
using control theory approach, we provide a theoretical method for analyzing
the synchronization of coupled nonidentical genetic oscillators. Sufficient
conditions for the synchronization as well as the estimation of the bound of
the synchronization error are also obtained. To demonstrate the effectiveness
of our theoretical results, a population of genetic oscillators based on the
Goodwin model are adopted as numerical examples.
