Mathematical Biosciences and Engineering, 2007, 4(4): 661-673. doi: 10.3934/mbe.2007.4.661.

Primary: 34C23, 34C25; Secondary: 92B20.

Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Modelling periodic oscillations during somitogenesis

1. Department of Physical Sciences and Mathematics, Florida Gulf Coast University, 10501 FGCU Blvd. S., Fort Myers, FL 33965

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 underwhich 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.
  Article Metrics

Keywords somitogenesis; pattern formation.; delay differential equations

Citation: Peng Feng, Menaka Navaratna. Modelling periodic oscillations during somitogenesis. Mathematical Biosciences and Engineering, 2007, 4(4): 661-673. doi: 10.3934/mbe.2007.4.661


This article has been cited by

  • 1. Guifang Fu, Zhong Wang, Jiahan Li, Rongling Wu, A mathematical framework for functional mapping of complex phenotypes using delay differential equations, Journal of Theoretical Biology, 2011, 289, 206, 10.1016/j.jtbi.2011.08.002
  • 2. Kanu Wahi, Matthew S. Bochter, Susan E. Cole, The many roles of Notch signaling during vertebrate somitogenesis, Seminars in Cell & Developmental Biology, 2016, 49, 68, 10.1016/j.semcdb.2014.11.010
  • 3. Kanu Wahi, Sophia Friesen, Vincenzo Coppola, Susan E. Cole, Putative binding sites for mir-125 family miRNAs in the mouse Lfng 3′UTR affect transcript expression in the segmentation clock, but mir-125a-5p is dispensable for normal somitogenesis, Developmental Dynamics, 2017, 246, 10, 740, 10.1002/dvdy.24552
  • 4. Robert P. Jenkins, Anja Hanisch, Cristian Soza-Ried, Erik Sahai, Julian Lewis, Arthur D Lander, Stochastic Regulation of her1/7 Gene Expression Is the Source of Noise in the Zebrafish Somite Clock Counteracted by Notch Signalling, PLOS Computational Biology, 2015, 11, 11, e1004459, 10.1371/journal.pcbi.1004459
  • 5. Hiroshi Momiji, Nicholas A.M. Monk, Dissecting the dynamics of the Hes1 genetic oscillator, Journal of Theoretical Biology, 2008, 254, 4, 784, 10.1016/j.jtbi.2008.07.013
  • 6. Lidan Sun, Rongling Wu, Mapping complex traits as a dynamic system, Physics of Life Reviews, 2015, 13, 155, 10.1016/j.plrev.2015.02.007
  • 7. Luis G. Morelli, Saúl Ares, Leah Herrgen, Christian Schröter, Frank Jülicher, Andrew C. Oates, Delayed coupling theory of vertebrate segmentation, HFSP Journal, 2009, 3, 1, 55, 10.2976/1.3027088
  • 8. Aitor González, Ryoichiro Kageyama, Hopf bifurcation in the presomitic mesoderm during the mouse segmentation, Journal of Theoretical Biology, 2009, 259, 1, 176, 10.1016/j.jtbi.2009.02.007
  • 9. Kang-Ling Liao, Chih-Wen Shih, Jui-Pin Tseng, Synchronized oscillations in a mathematical model of segmentation in zebrafish, Nonlinearity, 2012, 25, 4, 869, 10.1088/0951-7715/25/4/869

Reader Comments

your name: *   your email: *  

Copyright Info: 2007, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved