Nonlinear Dynamics

, Volume 76, Issue 1, pp 147–159 | Cite as

Oscillatory dynamics in a gene regulatory network mediated by small RNA with time delay

  • Haihong Liu
  • Fang Yan
  • Zengrong Liu
Original Paper


A genetic regulatory network mediated by small RNA with two time delays is investigated. We show by mathematical analysis and simulation that time delays can provide a mechanism for the intracellular oscillator. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of the positive equilibrium is investigated and Hopf bifurcations are demonstrated. Furthermore, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations. Finally, some numerical simulations are carried out for illustrating the theoretical results.


Small RNA Time delay Hopf bifurcation Periodic solution Oscillator 



The authors of this paper express their grateful gratitude for any helpful suggestions from reviewers and the partial support of the National Natural Science Foundation of China (11172158) and Yunnan Natural Science Foundation (2011FZ086) and the First-class Discipline of Universities in Shanghai


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of mathematicsYunnan Normal UniversityKunmingP.R. China
  2. 2.Institute of systems biologyShanghai UniversityShanghaiP.R. China
  3. 3.Department of mathematicsShanghai UniversityShanghaiP.R. China

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