Mathematics of the Genome


DOI: 10.1007/s10208-016-9316-x

Cite this article as:
Rajapakse, I. & Smale, S. Found Comput Math (2016). doi:10.1007/s10208-016-9316-x


This work gives a mathematical foundation for bifurcation from a stable equilibrium in the genome. We construct idealized dynamics associated with the genome. For this dynamics, we investigate the two main bifurcations from a stable equilibrium. Finally, we give mathematical proofs of existence and points of bifurcation for the repressilator and the toggle gene circuits.


Genome dynamics Gene networks Pitchfork bifurcation  Hopf bifurcation 

Mathematics Subject Classification

37G15 92D10 

Copyright information

© SFoCM 2016

Authors and Affiliations

  1. 1.University of MichiganAnn ArborUSA
  2. 2.City University of Hong KongKowloonHong Kong
  3. 3.Mathematics, University of CaliforniaBerkeleyUSA

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