Genetic oscillation deduced from Hopf bifurcation in a genetic regulatory network with delays.

  title={Genetic oscillation deduced from Hopf bifurcation in a genetic regulatory network with delays.},
  author={Min Xiao and Jinde Cao},
  journal={Mathematical biosciences},
  volume={215 1},
To understand how a gene regulatory network functioning as an oscillator is built, a genetic regulatory network with two transcriptional delays is investigated. We show by mathematical analysis and simulation that autorepression of mRNA and protein can provide a mechanism for the intracellular oscillator. Based on the linear stability approach and bifurcation theory, sufficient conditions for the oscillation of the genetic networks are derived, and critical values of Hopf bifurcation are… CONTINUE READING
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