数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (6): 2478-2504.doi: 10.1007/s10473-022-0617-7

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SYMBOLIC COMPUTATION FOR THE QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS

Bo HUANG1, Wei NIU2,3, Dongming WANG4,5   

  1. 1. LMIB-School of Mathematical Sciences, Beihang University, Beijing 100191, China;
    2. Ecole Centrale de Pékin, Beihang University, Beijing 100191, China;
    3. Beihang Hangzhou Innovation Institute Yuhang, Hangzhou 310051, China;
    4. LMIB-Institute of Artificial Intelligence, Beihang University, Beijing 100191, China;
    5. Centre National de la Recherche Scientifique, 75794 Paris Cedex 16, France
  • 收稿日期:2022-08-18 出版日期:2022-12-25 发布日期:2022-12-16
  • 通讯作者: Wei NIU, E-mail: Wei.Niu@buaa.edu.cn E-mail:Wei.Niu@buaa.edu.cn
  • 基金资助:
    The work was partially supported by the National Natural Science Foundation of China (12101032, 12131004 and 11601023), Ministry of Science and Technology of China (2021YFA1003600), and Beijing Natural Science Foundation (1212005).

SYMBOLIC COMPUTATION FOR THE QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS

Bo HUANG1, Wei NIU2,3, Dongming WANG4,5   

  1. 1. LMIB-School of Mathematical Sciences, Beihang University, Beijing 100191, China;
    2. Ecole Centrale de Pékin, Beihang University, Beijing 100191, China;
    3. Beihang Hangzhou Innovation Institute Yuhang, Hangzhou 310051, China;
    4. LMIB-Institute of Artificial Intelligence, Beihang University, Beijing 100191, China;
    5. Centre National de la Recherche Scientifique, 75794 Paris Cedex 16, France
  • Received:2022-08-18 Online:2022-12-25 Published:2022-12-16
  • Contact: Wei NIU, E-mail: Wei.Niu@buaa.edu.cn E-mail:Wei.Niu@buaa.edu.cn
  • Supported by:
    The work was partially supported by the National Natural Science Foundation of China (12101032, 12131004 and 11601023), Ministry of Science and Technology of China (2021YFA1003600), and Beijing Natural Science Foundation (1212005).

摘要: This paper provides a survey on symbolic computational approaches for the analysis of qualitative behaviors of systems of ordinary differential equations, focusing on symbolic and algebraic analysis for the local stability and bifurcation of limit cycles in the neighborhoods of equilibria and periodic orbits of the systems, with a highlight on applications to computational biology.

关键词: biological systems, center-focus, limit cycles, qualitative analysis, symbolic computation

Abstract: This paper provides a survey on symbolic computational approaches for the analysis of qualitative behaviors of systems of ordinary differential equations, focusing on symbolic and algebraic analysis for the local stability and bifurcation of limit cycles in the neighborhoods of equilibria and periodic orbits of the systems, with a highlight on applications to computational biology.

Key words: biological systems, center-focus, limit cycles, qualitative analysis, symbolic computation

中图分类号: 

  • 34C07