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Symbolic computation for the qualitative theory of differential equations

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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.

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Acknowledgments

The first author wishes to thank Xianbo Sun for providing him with helpful references on recent developments regarding Liénard systems.

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Authors and Affiliations

  1. LMIB - School of Mathematical Sciences, Beihang University, Beijing, 100191, China

    Bo Huang

  2. Ecole Centrale de Pékin, Beihang University, Beijing, 100191, China

    Wei Niu

  3. Beihang Hangzhou Innovation Institute Yuhang, Hangzhou, 310051, China

    Wei Niu

  4. LMIB - Institute of Artificial Intelligence, Beihang University, Beijing, 100191, China

    Dongming Wang

  5. Centre National de la Recherche Scientifique, 75794, Paris Cedex 16, France

    Dongming Wang

Authors
  1. Bo Huang
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  2. Wei Niu
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  3. Dongming Wang
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Corresponding author

Correspondence to Wei Niu.

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Dedicated to Professor Banghe LI on the Occasion of his 80th birthday

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).

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Huang, B., Niu, W. & Wang, D. Symbolic computation for the qualitative theory of differential equations. Acta Math Sci 42, 2478–2504 (2022). https://doi.org/10.1007/s10473-022-0617-7

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  • DOI: https://doi.org/10.1007/s10473-022-0617-7

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