Modelling periodic oscillations during somitogenesis
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Department of Physical Sciences and Mathematics, Florida Gulf Coast University, 10501 FGCU Blvd. S., Fort Myers, FL 33965
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Received:
01 July 2007
Accepted:
29 June 2018
Published:
01 August 2007
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MSC :
Primary: 34C23, 34C25; Secondary: 92B20.
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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.
Citation: Peng Feng, Menaka Navaratna. Modelling periodic oscillations during somitogenesis[J]. Mathematical Biosciences and Engineering, 2007, 4(4): 661-673. doi: 10.3934/mbe.2007.4.661
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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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