Synchronization of stochastic genetic oscillator networks with time delays and Markovian jumping parameters

Authors:
Yao Wang;Zidong Wang;Jinling Liang;Yurong Li;Min Du
Affiliations:
School of Information Science and Technology, Donghua University, Shanghai 200051, China;School of Information Science and Technology, Donghua University, Shanghai 200051, China and Department of Information Systems and Computing, Brunel University, Uxbridge, Middlesex UB8 3PH, UK;Department of Mathematics, Southeast University, Nanjing 210096, China;Department of Electrical Engineering, Fuzhou University, Fuzhou 350002, China;Department of Electrical Engineering, Fuzhou University, Fuzhou 350002, China
Venue:
Neurocomputing
Year:
2010

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Abstract

Genetic oscillator networks (GONs) are inherently coupled complex systems where the nodes indicate the biochemicals and the couplings represent the biochemical interactions. This paper is concerned with the synchronization problem of a general class of stochastic GONs with time delays and Markovian jumping parameters, where the GONs are subject to both the stochastic disturbances and the Markovian parameter switching. The regulatory functions of the addressed GONs are described by the sector-like nonlinear functions. By applying up-to-date 'delay-fractioning' approach for achieving delay-dependent conditions, we construct novel matrix functional to derive the synchronization criteria for the GONs that are formulated in terms of linear matrix inequalities (LMIs). Note that LMIs are easily solvable by the Matlab toolbox. A simulation example is used to demonstrate the synchronization phenomena within biological organisms of a given GON and therefore shows the applicability of the obtained results.