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OCLC Number 1128191733
Author Prathom, Kiattisak
Title Stability regions of cyclic solutions under negative feedback and uniqueness of periodic solutions for uneven cluster systems / Kiattisak Prathom
Imprint Ohio : Ohio University, 2019
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Description 1 online resource
Note Title from PDF title page
Full text release has been delayed at the author's request until September 01, 2021
Thesis (Ph.D.)--Ohio University, August 2019
Bibliog. Includes bibliographical references
Note Available online via OhioLINK's ETD center
System requirements: Adobe Acrobat Reader
Mode of Access: World Wide Web
Summary We study a simple model of many cells in a bioreactor in which cells in one part of the cycle called the signaling region may affect the growth rate of other cells in another part called the responsive region. The influence of one part to another is represented by a feedback function. For negative feedback, the model predicted that temporal clusters would be formed by groups of cells. Primarily we consider the cell cycle model under the condition that each cluster has the same size. We focus on regions of stability in parameter space of special periodic solutions corresponding to clustered configurations that are invariant under cyclic permutations of the clusters. The regions of stability coincide with ̀€̀€isosequential regions", triangular regions whose vertices are points where certain events in a solution occur simultaneously. For isosequential regions with a vertex touching the boundary of the parameter triangle, we prove that a cyclic periodic solution in an isosequential region is asymptotically stable in the clustered subspace if its index is relatively prime with respect to the number of clusters k and neutral otherwise
Subject Stability
Feedback control systems
Cluster analysis
Cell interaction
Academic theses.
Alt Author Ohio University. OUD Theses. Mathematics
OhioLINK Electronic Theses and Dissertations Center
OCLC Number 1128191733

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