Modelling periodic oscillations during somitogenesis

Peng Feng; Menaka Navaratna

doi:10.3934/mbe.2007.4.661

Article Contents

2007, Volume 4, Issue 4: 661-673. Doi: 10.3934/mbe.2007.4.661

This issue Previous Article Optimal control on hybrid ODE Systems with application to a tick disease model Next Article Final and peak epidemic sizes for SEIR models with quarantine and isolation

Modelling periodic oscillations during somitogenesis

Peng Feng^1, and
Menaka Navaratna^1,

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

Received: June 30, 2007

Revised: June 30, 2007

Published: July 2007

Abstract Related Papers Cited by

Abstract

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.

Keywords:

Mathematics Subject Classification: Primary: 34C23, 34C25; Secondary: 92B20.

Citation:

Article Metrics

HTML views() PDF downloads(40) Cited by(0)

Modelling periodic oscillations during somitogenesis

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Modelling periodic oscillations during somitogenesis

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content