Stability Analysis of Fuzzy Genetic Regulatory Networks with Various Time Delays

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Abstract

The synthetic genetic regulatory networks (GRNs) prove to be a powerful tool in studying gene regulation processes in living organisms. In order to take vagueness into consideration, fuzzy theory is incorporated in the GRNs and we found a novel system, namely fuzzy genetic regulatory networks (FGRNs). By applying the Homeomorphism theorem, we demonstrated an existence, uniqueness, and asymptotic stability analysis of the equilibrium point of FGRNs with time delay in the leakage term and unbounded distributed delays. By utilizing Lyapunov functional method and the linear matrix inequality (LMI) techniques, some new and useful criteria of the FGRNs with respect to the equilibrium point are derived. The derived criteria are of the form of LMI, and hence they can be verified easily. Finally, illustrative example with simulations are demonstrated to prove the effectiveness of the proposed results.

Keywords

Asymptotic stability Fuzzy genetic regulatory networks Homeomorphism theorem Leakage delay Linear matrix inequality 

Mathematics Subject Classification

93D20 94D05 65L20 92C42 
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Notes

Acknowledgments

This work was supported by the University of Malaya HIR Grant UM.C/625/1/HIR/MOHE/SC/13. Moreover, the authors would like to thank the Editor-in-Chief and the anonymous reviewers for their constructive comments and fruitful suggestions to improve the quality of the manuscript.

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2016

Authors and Affiliations

  1. 1. Faculty of Science, Institute of Mathematical SciencesUniversity of MalayaKuala LumpurMalaysia
  2. 2.Department of MathematicsGandhigram Rural Institute - Deemed UniversityGandhigramIndia

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