Synchronization of coupled nonidentical genetic oscillators.
The study of 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 a control theory approach, we provide a theoretical method for analysing 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.
ERATO Aihara Complexity Modelling Project, JST, Room M204, Komaba Open Laboratory, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan. cgli@uestc.edu.cn
Chunguang
C
Li
Luonan
L
Chen
Kazuyuki
K
Aihara
D001683:Biological Clocks; D003198:Computer Simulation; D005786:Gene Expression Regulation; D008962:Models, Theoretical; D009991:Oscillometry