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Qualitative investigation of a gene model using computer algebra algorithms

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Abstract

Using algorithms and packages for computer algebra, we investigate a three-dimensional autonomous system of ordinary differential equations (ODEs) used in [1] to simulate the dynamics of a gene. A computational approach based on elimination theory algorithms is proposed to find invariant surfaces of multidimensional polynomial differential equation systems; this approach allows one to reduce the investigation of the system dynamics to studying the dynamics of a lower-order system. In addition, an effective approach based on the Lyapunov function is proposed to investigate the Andronov-Hopf bifurcation; this approach is used to find such bifurcations in the model under study.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    M. Han & V. G. Romanovski

  2. Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, Maribor, SI-2000, Slovenia

    V. G. Romanovski

  3. Faculty of Natural Sciences and Mathematics, University of Maribor, Koroska c. 160, Maribor, SI-2000, Slovenia

    V. G. Romanovski

  4. LIFL, Universite Lille 1, 59655, Villeneuve d’Ascq, France

    F. Boulier & F. Lemaire

Authors
  1. F. Boulier
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  2. M. Han
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  3. F. Lemaire
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  4. V. G. Romanovski
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Correspondence to M. Han.

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Original Russian Text © F. Boulier, M. Han, F. Lemaire, V.G. Romanovski, 2015, published in Programmirovanie, 2015, Vol. 41, No. 2.

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Boulier, F., Han, M., Lemaire, F. et al. Qualitative investigation of a gene model using computer algebra algorithms. Program Comput Soft 41, 105–111 (2015). https://doi.org/10.1134/S0361768815020048

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