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Heteroclinic cycles in the repressilator model

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  • Kuznetsov, A.
  • Afraimovich, V.

Abstract

A repressilator is a synthetic regulatory network that produces self-sustained oscillations. We analyze the evolution of the oscillatory solution in the repressilator model. We have established a connection between the evolution of the oscillatory solution and formation of a heteroclinic cycle at infinity. The convergence of the limit cycle to the heteroclinic cycle occurs very differently compared to the well-studied cases. The transition studied here presents a new bifurcation scenario.

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  • Kuznetsov, A. & Afraimovich, V., 2012. "Heteroclinic cycles in the repressilator model," Chaos, Solitons & Fractals, Elsevier, vol. 45(5), pages 660-665.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:5:p:660-665
    DOI: 10.1016/j.chaos.2012.02.009
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    References listed on IDEAS

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    1. Michael B. Elowitz & Stanislas Leibler, 2000. "A synthetic oscillatory network of transcriptional regulators," Nature, Nature, vol. 403(6767), pages 335-338, January.
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    2. Svetoslav G. Nikolov & Vassil M. Vassilev, 2021. "Dynamics of Rössler Prototype-4 System: Analytical and Numerical Investigation," Mathematics, MDPI, vol. 9(4), pages 1-17, February.

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