Journal of Mathematical Biology

, Volume 72, Issue 6, pp 1607–1632 | Cite as

Scale invariance analysis for genetic networks applying homogeneity

  • Emmanuel Bernuau
  • Denis EfimovEmail author
  • Wilfrid Perruquetti


Scalability is a property describing the change of the trajectory of a dynamical system under a scaling of the input stimulus and of the initial conditions. Particular cases of scalability include the scale invariance and fold change detection (when the scaling of the input does not influence the system output). In the present paper it is shown that homogeneous systems have this scalability property while locally homogeneous systems approximately possess this property. These facts are used for detecting scale invariance or approximate scalability (far from a steady state) in several biological systems. The results are illustrated by various regulatory networks.

Mathematics Subject Classification

92D25 37C75 37C80 34D20 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Emmanuel Bernuau
    • 3
  • Denis Efimov
    • 1
    • 2
    • 4
    Email author
  • Wilfrid Perruquetti
    • 1
    • 2
  1. 1.Non-A Team, Inria Lille, Parc Scientifique de la Haute BorneVilleneuve d’AscqFrance
  2. 2.CRIStAL, UMR-CNRS 9189, Ecole Centrale de LilleVilleneuve-d’AscqFrance
  3. 3.Faculty of EngineeringUniversity of PisaPisaItaly
  4. 4.Department of Control Systems and InformaticsNational Research University ITMOSaint PetersburgRussia

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