Existence criteria of periodic oscillations in cyclic gene regulatory networks

@article{Hori2011ExistenceCO,
  title={Existence criteria of periodic oscillations in cyclic gene regulatory networks},
  author={Yutaka Hori and Tae-Hyoung Kim and Shinji Hara},
  journal={Automatica},
  year={2011},
  volume={47},
  pages={1203-1209}
}
In this paper, we derive graphical and analytic criteria for the existence of periodic oscillations in large-scale cyclic gene regulatory networks, and present quantitative biological insight based on the analytic result. Based on the Poincaré-Bendixson theorem for cyclic systems, it is first shown that local instability of an equilibrium point implies the existence of periodic oscillations. Then, we prove that local instability of the heterogeneous gene regulatory network system, where… CONTINUE READING

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