Existence criteria of periodic oscillations in cyclic gene regulatory networks

Yutaka Hori, Tae Hyoung Kim, Shinji Hara

Research output: Contribution to journalArticlepeer-review

48 Citations (Scopus)


In this paper, we consider the existence conditions of periodic oscillations in large-scale cyclic gene regulatory networks. Using the PoincarBendixson theorem for cyclic systems, we first show that the local instability of an equilibrium point implies the existence of periodic oscillations. We then derive the graphical and its equivalent analytic criteria for the existence of periodic oscillations based on local instability analysis. These criteria have a remarkable feature that they can be applied systematically to a large-scale cyclic gene regulatory network consisting of any number of genes. The latter part of this paper is devoted to analyze the relation between an equilibrium point and the biochemical parameters. This leads to an analytic existence criterion that explicitly takes the dependence of the equilibrium state on biochemical parameters into account, which is often overlooked in nonlinear system analyses. In particular, the novel physical quantities that are essential for determining the existence of periodic oscillations are obtained based on the rigorous analytic criterion.

Original languageEnglish
Pages (from-to)1203-1209
Number of pages7
Issue number6
Publication statusPublished - 2011 Jun
Externally publishedYes


  • Gene regulatory network
  • Large-scale systems
  • Nonlinear systems
  • Periodic oscillation
  • Systems biology

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


Dive into the research topics of 'Existence criteria of periodic oscillations in cyclic gene regulatory networks'. Together they form a unique fingerprint.

Cite this