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
相关论文
共 50 条
  • [21] Symbolic computation of exact solutions for nonlinear evolution equations
    Zhang, Lei
    Lin, Yezhi
    NONLINEAR DYNAMICS, 2015, 79 (02) : 823 - 833
  • [22] Improving the averaging theory for computing periodic solutions of the differential equations
    Llibre, Jaume
    Novaes, Douglas D.
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2015, 66 (04): : 1401 - 1412
  • [23] Improving the averaging theory for computing periodic solutions of the differential equations
    Jaume Llibre
    Douglas D. Novaes
    Zeitschrift für angewandte Mathematik und Physik, 2015, 66 : 1401 - 1412
  • [24] Generalized multiple Riccati equations rational expansion method with symbolic computation to construct exact complexiton solutions of nonlinear partial differential equations
    Li, Wenting
    Zhang, Hongqing
    APPLIED MATHEMATICS AND COMPUTATION, 2008, 197 (01) : 288 - 296
  • [25] On establishing qualitative theory to nonlinear boundary value problem of fractional differential equations
    Amjad Ali
    Nabeela Khan
    Seema Israr
    Mathematical Sciences, 2021, 15 : 395 - 403
  • [26] On establishing qualitative theory to nonlinear boundary value problem of fractional differential equations
    Ali, Amjad
    Khan, Nabeela
    Israr, Seema
    MATHEMATICAL SCIENCES, 2021, 15 (04) : 395 - 403
  • [27] Traveling wave solutions for nonlinear equations using symbolic computation
    Fan, EG
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2002, 43 (6-7) : 671 - 680
  • [28] Soliton interactions for coupled nonlinear Schrodinger equations with symbolic computation
    Liu, Wen-Jun
    Pan, Nan
    Huang, Long-Gang
    Lei, Ming
    NONLINEAR DYNAMICS, 2014, 78 (01) : 755 - 770
  • [29] Bounding the number of limit cycles for parametric Li?nard systems using symbolic computation methods
    Hu, Yifan
    Niu, Wei
    Huang, Bo
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2021, 96
  • [30] Travelling wave solutions of nonlinear evolution equations by using symbolic computation
    Engui F.
    Applied Mathematics-A Journal of Chinese Universities, 2001, 16 (2) : 149 - 155
12345