Global stability analysis and robust design of multi-time-scale biological networks under parametric uncertainties

Anke Meyer-Baese, Ali J. Koshkouei, Mark R. Emmett, David P. Goodall

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Biological networks are prone to internal parametric fluctuations and external noises. Robustness represents a crucial property of these networks, which militates the effects of internal fluctuations and external noises. In this paper biological networks are formulated as coupled nonlinear differential systems operating at different time-scales under vanishing perturbations. In contrast to previous work viewing biological parametric uncertain systems as perturbations to a known nominal linear system, the perturbed biological system is modeled as nonlinear perturbations to a known nonlinear idealized system and is represented by two time-scales (subsystems). In addition, conditions for the existence of a global uniform attractor of the perturbed biological system are presented. By using an appropriate Lyapunov function for the coupled system, a maximal upper bound for the fast time-scale associated with the fast state is derived. The proposed robust system design principles are potentially applicable to robust biosynthetic network design. Finally, two examples of two important biological networks, a neural network and a gene regulatory network, are presented to illustrate the applicability of the developed theoretical framework.

Original languageEnglish (US)
Pages (from-to)658-663
Number of pages6
JournalNeural Networks
Issue number5-6
StatePublished - Jul 2009
Externally publishedYes


  • Multi-time-scale neural network
  • Parametric uncertainties
  • Regulatory gene network
  • Robust stability

ASJC Scopus subject areas

  • Cognitive Neuroscience
  • Artificial Intelligence


Dive into the research topics of 'Global stability analysis and robust design of multi-time-scale biological networks under parametric uncertainties'. Together they form a unique fingerprint.

Cite this