Passivity of Reaction–Diffusion Genetic Regulatory Networks with Time-Varying Delays

Passivity of Reaction–Diffusion Genetic Regulatory Networks with Time-Varying Delays This article investigates the passivity of reaction–diffusion genetic regulatory networks (GRNs) with time-varying delays and uncertainty terms under Dirichlet, Neumann, and Robin boundary conditions. We provide delay-dependent stability criteria by constructing appropriate Lyapunov–Krasovskii functions and linear matrix inequalities, and offer conditions sufficient to ensure the passivity of GRNs. We conducted a comparative analysis of GRNs under these three conditions. Numerical examples of the proposed approaches are provided to illustrate its effectiveness, and represent the three-dimensional figures of the trajectories of the concentrations of mRNA and the proteins of GRNs under Dirichlet boundary conditions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Neural Processing Letters Springer Journals

Passivity of Reaction–Diffusion Genetic Regulatory Networks with Time-Varying Delays

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media, LLC
Subject
Computer Science; Artificial Intelligence (incl. Robotics); Complex Systems; Computational Intelligence
ISSN
1370-4621
eISSN
1573-773X
D.O.I.
10.1007/s11063-017-9682-7
Publisher site
See Article on Publisher Site

Abstract

This article investigates the passivity of reaction–diffusion genetic regulatory networks (GRNs) with time-varying delays and uncertainty terms under Dirichlet, Neumann, and Robin boundary conditions. We provide delay-dependent stability criteria by constructing appropriate Lyapunov–Krasovskii functions and linear matrix inequalities, and offer conditions sufficient to ensure the passivity of GRNs. We conducted a comparative analysis of GRNs under these three conditions. Numerical examples of the proposed approaches are provided to illustrate its effectiveness, and represent the three-dimensional figures of the trajectories of the concentrations of mRNA and the proteins of GRNs under Dirichlet boundary conditions.

Journal

Neural Processing LettersSpringer Journals

Published: Aug 14, 2017

References

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