Symbolic computation for the qualitative theory of differential equations

被引：2
|
作者：
Huang, Bo [1 ]
Niu, Wei [2 ,3 ]
Wang, Dongming [4 ,5 ]
机构：
[1] Beihang Univ, LMIB Sch Math Sci, Beijing 100191, Peoples R China
[2] Beihang Univ, Ecole Cent Pekin, Beijing 100191, Peoples R China
[3] Beihang Hangzhou Innovat Inst Yuhang, Hangzhou 310051, Peoples R China
[4] Beihang Univ, LMIB Inst Artificial Intelligence, Beijing 100191, Peoples R China
[5] Ctr Natl Rech Sci, F-75794 Paris 16, France
来源：
ACTA MATHEMATICA SCIENTIA | 2022年 / 42卷 / 06期
基金：
北京市自然科学基金; 中国国家自然科学基金;
关键词：
biological systems; center-focus; limit cycles; qualitative analysis; symbolic computation; ELLIPTIC HAMILTONIAN-SYSTEMS; STEADY-STATE LAWS; LIMIT-CYCLES; CUBIC SYSTEM; HOPF BIFURCATIONS; POLYNOMIAL SYSTEMS; NORMAL FORMS; SMALL PERTURBATIONS; STABILITY ANALYSIS; AVERAGING THEORY;
D O I：
10.1007/s10473-022-0617-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
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.
引用
收藏
页码：2478 / 2504
页数：27
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