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      Stability analysis of a dynamical model representing gene regulatory networks

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      Author(s)
      Ahsen, M. E.
      Özbay, Hitay
      Niculescu, S. I.
      Date
      2012
      Source Title
      International Federation of Automatic Control IFAC Proceedings Volumes
      Print ISSN
      1474-6670
      Volume
      10
      Issue
      14
      Pages
      191 - 196
      Language
      English
      Type
      Conference Paper
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      Abstract
      In this paper we perform stability analysis of a class of cyclic biological processes involving time delayed feedback. More precisely, we analyze the genetic regulatory network having nonlinearities with negative Schwarzian derivatives. We derive a set of conditions implying global stability of the genetic regulatory network under positive feedback. As a special case, we also consider homogenous genetic regulatory networks and obtain an appropriate stability condition which depends only on the parameters of the nonlinearity function. © 2012 IFAC.
      Keywords
      Asymptotic stability
      Gene regulatory networks
      Hill functions
      Nonlinear time delay networks
      Schwarzian derivatives
      Biological process
      Dynamical model
      Gene regulatory networks
      Genetic regulatory networks
      Global stability
      Hill function
      Nonlinear time delays
      Nonlinearity function
      Schwarzian derivative
      Stability analysis
      Stability condition
      Time-delayed feedback
      Asymptotic stability
      Genes
      Time delay
      Permalink
      http://hdl.handle.net/11693/28165
      Published Version (Please cite this version)
      https://doi.org/10.3182/20120622-3-US-4021.00020
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      • Department of Electrical and Electronics Engineering 3702
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