Symbolic computation for the qualitative theory of differential equations

Bo Huang; Wei Niu; Dongming Wang

doi:10.1007/s10473-022-0617-7

Symbolic computation for the qualitative theory of differential equations

Bo Huang
, Wei Niu^*
, Dongming Wang

^*Corresponding author for this work

Beihang Hangzhou Innovation Institute Yuhang
CNRS

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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.

Original language	English
Pages (from-to)	2478-2504
Number of pages	27
Journal	Acta Mathematica Scientia
Volume	42
Issue number	6
DOIs	https://doi.org/10.1007/s10473-022-0617-7
State	Published - Nov 2022

Keywords

34C07
37G15
68W30
biological systems
center-focus
limit cycles
qualitative analysis
symbolic computation

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10.1007/s10473-022-0617-7

Cite this

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title = "Symbolic computation for the qualitative theory of differential equations",

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.",

keywords = "34C07, 37G15, 68W30, biological systems, center-focus, limit cycles, qualitative analysis, symbolic computation",

author = "Bo Huang and Wei Niu and Dongming Wang",

note = "Publisher Copyright: {\textcopyright} 2022, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences.",

year = "2022",

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doi = "10.1007/s10473-022-0617-7",

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AU - Wang, Dongming

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AB - 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.

KW - 34C07

KW - 37G15

KW - 68W30

KW - biological systems

KW - center-focus

KW - limit cycles

KW - qualitative analysis

KW - symbolic computation

UR - https://www.scopus.com/pages/publications/85139691351

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DO - 10.1007/s10473-022-0617-7

M3 - 文章

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EP - 2504

JO - Acta Mathematica Scientia

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Symbolic computation for the qualitative theory of differential equations

Abstract

Keywords

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