Foundations of Computational Mathematics

, Volume 17, Issue 5, pp 1195–1217 | Cite as

Mathematics of the Genome



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 



We would like to thank Yan Jun, Lu Zhang, Lindsey Muir, Geoff Patterson, Xin Guo, Anthony Bloch, an anonymous referee and especially Mike Shub for helpful discussions. We extend thanks to James Gimlett and Srikanta Kumar at Defense Advanced Research Projects Agency for support and encouragement.


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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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