Existence of Limit Cycles in the Repressilator Equations

@article{Buse2009ExistenceOL,
  title={Existence of Limit Cycles in the Repressilator Equations},
  author={Olguta Buse and Alexey Kuznetsov and Rodrigo A. P{\'e}rez},
  journal={I. J. Bifurcation and Chaos},
  year={2009},
  volume={19},
  pages={4097-4106}
}
The Repressilator is a genetic regulatory network used to model oscillatory behavior of more complex regulatory networks like the circadian clock. We prove that the Repressilator equations undergo a supercritical Hopf bifurcation as the maximal rate of protein synthesis increases, and find a large range of parameters for which there is a cycle. 

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