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Synchronization in networks of genetic oscillators with delayed coupling
Author(s) -
Li Ping,
Lam James
Publication year - 2011
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.360
Subject(s) - synchronization (alternating current) , coupling (piping) , control theory (sociology) , synchronization networks , computer science , topology (electrical circuits) , computer simulation , control (management) , mathematics , engineering , simulation , artificial intelligence , mechanical engineering , combinatorics
This paper studies the global synchronization problem for gene networks of coupled oscillators with a coupling delay. Several synchronization conditions are obtained for coupled genetic oscillators by means of Lyapunov functional theory and matrix inequality approach. More specifically, two conditions are first presented in terms of matrix inequalities, under which the synchronization can be achieved irrespective of how large the coupling delay is. Then, a sufficient condition is further proposed to ensure the synchronization of coupled genetic oscillators for a certain range of coupling delays. A numerical example of coupled Goodwin oscillators is given to illustrate the effectiveness of these conditions. Both theoretical and numerical results show that the coupling delay can affect the dynamic behaviors of coupled genetic oscillators, and the synchronized state can be significantly different from that of a single oscillator when a coupling delay is present. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society