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Modelling periodic oscillations during somitogenesis.

Peng Feng1, Menaka Navaratna

  • 1Department of Physical Sciences and Mathematics, Florida Gulf Coast University, 10501 FGCU Blvd. S., Fort Myers, FL 33965, USA. pfeng@fgcu.edu

Mathematical Biosciences and Engineering : MBE
|October 11, 2007
PubMed
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This study analyzes a genetic network model using delay differential equations. It identifies conditions for stability loss and Hopf bifurcations, leading to sustained oscillations in genetic networks.

Area of Science:

  • Systems Biology
  • Mathematical Biology
  • Genetics

Background:

  • The study examines a previously established J. Lewis genetic network model.
  • This model is formulated using delay differential equations incorporating two distinct time delays.

Purpose of the Study:

  • To determine conditions for the local stability of the non-trivial steady state within the genetic network model.
  • To investigate the mechanisms and thresholds leading to the loss of stability and the emergence of oscillations.

Main Methods:

  • Analysis of delay differential equations to derive stability conditions.
  • Investigation of Hopf bifurcation as a mechanism for oscillation onset.
  • Numerical simulations to explore parameter influences on oscillation characteristics.

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Main Results:

  • Conditions for local stability of the non-trivial steady state are established.
  • A critical ratio of time delays is identified as the trigger for sustained oscillations via Hopf bifurcation.
  • Numerical simulations reveal how parameters affect oscillation period and amplitude.

Conclusions:

  • The research provides a theoretical framework for understanding oscillatory behavior in genetic networks.
  • Hopf bifurcation is confirmed as a key mechanism driving oscillations in this model.
  • Parameter-dependent modulation of oscillation characteristics is demonstrated, with implications for network dynamics.