Modelling periodic oscillations during somitogenesis

Peng Feng; Menaka Navaratna

doi:10.3934/mbe.2007.4.661

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

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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

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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.

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

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