Stability Analysis of Fuzzy Genetic Regulatory Networks with Various Time Delays

Ratnavelu, Kurunathan and Kalpana, Muthusamy and Balasubramaniam, Pagavathi (2018) Stability Analysis of Fuzzy Genetic Regulatory Networks with Various Time Delays. Bulletin of the Malaysian Mathematical Sciences Society, 41 (1). pp. 491-505. ISSN 0126-6705

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Official URL: https://doi.org/10.1007/s40840-016-0427-y

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.

Item Type: Article
Uncontrolled Keywords: Asymptotic stability; Fuzzy genetic regulatory networks; Homeomorphism theorem; Leakage delay; Linear matrix inequality
Subjects: Q Science > Q Science (General)
Q Science > QA Mathematics
Divisions: Faculty of Science > Institute of Mathematical Sciences
Depositing User: Ms. Juhaida Abd Rahim
Date Deposited: 15 Apr 2019 09:04
Last Modified: 15 Apr 2019 09:04
URI: http://eprints.um.edu.my/id/eprint/20909

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