Comments and Corrections on 'Stability of Genetic Regulatory Networks with Time Delay'

Masaaki Takada, Yutaka Hori, Shinji Hara

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


This paper shows that the necessary and sufficient condition for the local stability of gene regulatory networks with time delay (Theorem 2) presented in the highly cited paper [L. Chen and K. Aihara, IEEE TCAS-I, vol. 49, No. 5, pp. 602-608, 2002] is erroneous. An illustrative counterexample is presented, and it is pointed out that there are essentially two errors in their derivation. A corrected theorem is then derived using the approach shown in the aforementioned paper. It turns out that the corrected theorem provides only a sufficient condition for the local stability. Finally, a necessary and sufficient condition that was recently presented by the authors' of this paper is presented. Both the sufficient and the necessary and sufficient conditions are demonstrated using the Repressilator, the oscillatory gene regulatory network, which was also used for the illustration of the Chen and Aihara's original result.

Original languageEnglish
Article number6851213
Pages (from-to)2771-2774
Number of pages4
JournalIEEE Transactions on Circuits and Systems I: Regular Papers
Issue number9
Publication statusPublished - 2014 Sept
Externally publishedYes


  • Awards activities
  • Circuit stability
  • Delay effects
  • Eigenvalues and eigenfunctions
  • Gene regulatory networks
  • Local stability analysis
  • Proteins
  • Stability criteria
  • Time delay

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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