Skip to Main Content
 

Global Search Box

 
 
 

ETD Abstract Container

Abstract Header

Stability Regions of Cyclic Solutions under Negative Feedback and Uniqueness of Periodic Solutions for Uneven Cluster Systems

Prathom, Kiattisak
http://orcid.org/0000-0002-0463-8162
http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1562778288743268

Abstract Details

2019, Doctor of Philosophy (PhD), Ohio University, Mathematics (Arts and Sciences).
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. For negative linear feedback, we further prove that there is a stable cyclic periodic solution corresponding to any given point in the interior of the set of parameters. We consider separately the cell cycle model with two uneven clusters under negative feedback. When cells in the cycle are grouped in two clusters with different sizes, the values of the feedback function depends upon the sizes of clusters. We prove that the interval between the signaling and responsive regions determines the nature of the periodic solutions within the set of two clustered solutions. In particular, for any given sizes of the 2 clusters, there is a unique attracting 2-clustered periodic solution if this interval has length less than or equal to 1/2 and the system has an attracting interval of 2-clustered periodic solutions otherwise.
Todd Young (Advisor)
Winfried Just (Committee Member)
Martin Mohlenkamp (Committee Member)
Alexander Neiman (Committee Member)
181 p.
Mathematics
stability; cyclic solution; negative feedback; uneven cluster

Recommended Citations

Citations

  • Prathom, K. (2019). Stability Regions of Cyclic Solutions under Negative Feedback and Uniqueness of Periodic Solutions for Uneven Cluster Systems [Doctoral dissertation, Ohio University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1562778288743268

    APA Style (7th edition)

  • Prathom, Kiattisak. Stability Regions of Cyclic Solutions under Negative Feedback and Uniqueness of Periodic Solutions for Uneven Cluster Systems. 2019. Ohio University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1562778288743268.

    MLA Style (8th edition)

  • Prathom, Kiattisak. "Stability Regions of Cyclic Solutions under Negative Feedback and Uniqueness of Periodic Solutions for Uneven Cluster Systems." Doctoral dissertation, Ohio University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1562778288743268

    Chicago Manual of Style (17th edition)

ohiou1562778288743268
194
© 2019, all rights reserved.
This open access ETD is published by Ohio University and OhioLINK.