Modelling periodic oscillations during somitogenesis.
We consider a model of genetic network that has been previously presented by J. Lewis. This model takes the form of delay differential equations with two delays. We give conditions for the local stability of the non-trivial steady state. We investigate the condition under which stability is lost and oscillations occur. In particular, we show that when the ratio of the time delays passes a threshold, sustained oscillations occur through a Hopf bifurcation. Through numerical simulations, we further investigate the ways in which various parameters influence the period and the amplitude of the oscillations. In conclusion, we discuss the implications of our results.
Feng
Peng
P
Department of Physical Sciences and Mathematics, Florida Gulf Coast University, 10501 FGCU Blvd. S., Fort Myers, FL 33965, USA. pfeng@fgcu.edu
Navaratna
Menaka
M
D000818:Animals; D051792:Basic Helix-Loop-Helix Proteins / Q000096:biosynthesis / Q000235:genetics; D001683:Biological Clocks / Q000235:genetics / Q000502:physiology; D018507:Gene Expression Regulation, Developmental; D008957:Models, Genetic; D009716:Numerical Analysis, Computer-Assisted; D012333:RNA, Messenger / Q000096:biosynthesis / Q000235:genetics; D019170:Somites / Q000196:embryology*; D015027:Zebrafish / Q000196:embryology* / Q000235:genetics; D029961:Zebrafish Proteins / Q000096:biosynthesis / Q000235:genetics
D051792:Basic Helix-Loop-Helix Proteins; D012333:RNA, Messenger; D029961:Zebrafish Proteins; C491619:her1 protein, zebrafish