| In this talk, I will present recent mathematical
research towards understanding how vertebrate segmentation works.
Even in the most simple vertebrates, we have complicated gene
networks act in each cell that gives rise to oscillations, and cell
to cell communication through delta-notch pathway synchronizes these
oscillations. In this talk, we study the effects of time delays on
the dynamics of a segmentation clock model with both discrete and
distributed delays. Two cases are considered. The first case
corresponds to the model with only distributed delay. The second
case involves both discrete and distributed delay. Local stability
analysis is carried out for all cases. Numerical simulations are
also performed to illustrate the results. |