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Volume 41 Issue 12
Dec.  2015
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Journal of Beijing University of Aeronautics and Astronautics  > 2015  >  41(12): 2363-2369.
LIU Jun, NIU Wei. Analysis of all time-delay stability for biological systems using symbolic computation methods[J]. Journal of Beijing University of Aeronautics and Astronautics, 2015, 41(12): 2363-2369. doi: 10.13700/j.bh.1001-5965.2014.0794(in Chinese)
Citation: LIU Jun, NIU Wei. Analysis of all time-delay stability for biological systems using symbolic computation methods[J]. Journal of Beijing University of Aeronautics and Astronautics, 2015, 41(12): 2363-2369. doi: 10.13700/j.bh.1001-5965.2014.0794(in Chinese)
shu

Analysis of all time-delay stability for biological systems using symbolic computation methods

doi: 10.13700/j.bh.1001-5965.2014.0794

  • Sino-French Engineer School, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

  • Received Date: 17 Dec 2014
  • Rev Recd Date: 20 Mar 2015
  • Publish Date: 20 Dec 2015
    Abstract
  • All time-delay stability for biological systems shows that the time-delay system possess good reliability, so this issue has always been the highlight of the scholars research. However, researchers usually adopt the traditional mathematical methods or numerical calculation methods. Based on Hurwitz criterion and polynomial complete discriminant system, a sufficient and necessary algebraic criterion of all time-delay stability for nonlinear biological systems with parameters was introduced. By using symbolic computation methods, such as the methods of Grbner basis,triangular decomposition and real solution classification, a systematic and algorithmic approach for automatically analyzing all time-delay stability of biological systems with parameters was proposed. All the computations in our approach are all exact, which may help biologists and engineers to perform algebraic analysis for certain biological models. The successful experiments on the all time-delay stability analysis of several biological models, such as time delayed Lotka-Volterra systems and SIR epidemic models with time delay, showed the feasibility of our algebraic approach and also the superiority of symbolic computation methods compared with traditional mathematic methods.

     

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