Math-Biology Seminar | Covering by Stable Sub-Triangles in a Cell Cycle Model, April 2

Kiattisak Prathom

The Dynamical Systems and Mathematical Biology Seminar presents Kiattisak Prathom discussing “Covering by Stable Sub-Triangles in a Cell Cycle Model” on Tuesday, April 2, from 3:05 to 4 p.m., in Morton 326.

Prathom is a graduate student in Mathematics at Ohio University.

ABSTRACT:  We consider a dynamical system of cells/clusters in a cell cycle where the number of cells/cluster in the cycle is finite and the number of cells/clusters in one region affect the growth rate of cells/clusters in another region. We consider a simple cell cycle model with a feedback function and introduce a cyclic solution. Then, we investigate stability of the solutions and define asymptotically/neutrally stable regions corresponding to the cyclic solution. By some previous results, the regions are sub-triangles. A sub-triangle can be an asymptotic stable or neutrally stable or unstable region. In the talk, we will show that any point in the parameter triangle, {(s,r)|0<s<r<1}, is covered by a stable sub-triangle for the cell cycle model relating to zero and linear negative feedback functions.