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

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Abstract

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.

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Acknowledgement

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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Authors and Affiliations

  1. Department of mathematics, Yunnan Normal University, Kunming, 650092, P.R. China

    Haihong Liu & Fang Yan

  2. Institute of systems biology, Shanghai University, Shanghai, 200444, P.R. China

    Zengrong Liu

  3. Department of mathematics, Shanghai University, Shanghai, 200444, P.R. China

    Zengrong Liu

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  1. Haihong Liu
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  2. Fang Yan
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Correspondence to Zengrong Liu.

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Liu, H., Yan, F. & Liu, Z. Oscillatory dynamics in a gene regulatory network mediated by small RNA with time delay. Nonlinear Dyn 76, 147–159 (2014). https://doi.org/10.1007/s11071-013-1117-z

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