Programming and Computer Software

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

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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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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