Programming and Computer Software

, Volume 41, Issue 2, pp 105–111 | Cite as

Qualitative investigation of a gene model using computer algebra algorithms

  • F. Boulier
  • M. Han
  • F. Lemaire
  • V. G. Romanovski


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.


Singular Point Lyapunov Function Hopf Bifurcation Polynomial System Singular System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  • F. Boulier
    • 4
  • M. Han
    • 1
  • F. Lemaire
    • 4
  • V. G. Romanovski
    • 1
    • 2
    • 3
  1. 1.Department of MathematicsShanghai Normal UniversityShanghaiChina
  2. 2.Center for Applied Mathematics and Theoretical PhysicsUniversity of MariborMariborSlovenia
  3. 3.Faculty of Natural Sciences and MathematicsUniversity of MariborMariborSlovenia
  4. 4.LIFLUniversite Lille 1Villeneuve d’AscqFrance

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