A computational method for robust bifurcation analysis and its application to biomolecular systems

Masaki Inoue, Hikaru Ikuta, Shuichi Adachi, Jun Ichi Imura, Kazuyuki Aihara

Research output: Contribution to journalArticle


We consider a general uncertain nonlinear dynamical system defined in a certain model set, and reformulate a problem of robustness bifurcation analysis (RBA), which has been originally formulated in our previous work. As such, we develop an efficient computational method for the RBA, which can be used for quantitative evaluation of bifurcation robustness in uncertain dynamical systems. Specifically, we first linearize the uncertain system properly and then apply a feedback transformation technique to reduce the RBA problem to a linear robustness analysis one, which can be solved using μ-analysis, a common analysis technique in robust control theory. Finally, we provide robustness analysis of a gene regulatory network model where oscillatory behavior appears according to Hopf bifurcation. We give quantitative evaluation of the bifurcation robustness using the RBA method proposed here.

Original languageEnglish
Article number1540012
JournalInternational Journal of Bifurcation and Chaos
Issue number7
Publication statusPublished - 2015 Jun 30



  • Bifurcation theory
  • gene regulatory networks
  • robust control theory

ASJC Scopus subject areas

  • Applied Mathematics
  • General
  • Engineering(all)
  • Modelling and Simulation

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