HOPF BIFURCATIONS IN DYNAMICAL SYSTEMS VIA ALGEBRAIC TOPOLOGICAL METHOD

被引：0
作者：
Jawarneh, Ibrahim [1 ]
Altawallbeh, Zuhier [2 ]
机构：
[1] Al Hussein Bin Talal Univ, Dept Math, Maan 71111, Jordan
[2] Tafila Tech Univ, Dept Math, Tafila 66110, Jordan
来源：
MATEMATICKI VESNIK | 2023年 / 75卷 / 03期
关键词：
Supercritical Hopf bifurcation; subcritical Hopf bifurcation; stable limit cycle; unstable limit cycle; homological Conley index; Morse sets; ONE-PARAMETER FAMILIES; ORBITS; INDEX;
D O I：
10.57016/MV-rx451is8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A nonlinear phenomenon in nature is often modeled by a system of differential equations with parameters. The bifurcation occurs when a parameter varies in such systems, causing a qualitative change in its solution. In this paper, we study one of the most exciting bifurcations, which is Hopf bifurcation. We use tools from algebraic topology to analyze and reveal supercritical and subcritical Hopf bifurcations.
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收藏
页码：216 / 224
页数：9
相关论文
共 21 条
  • [11] EXISTENCE OF GENERALIZED HOMOCLINIC ORBITS FOR ONE PARAMETER FAMILIES OF FLOWS
    MISCHAIKOW, K
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 103 (01) : 59 - 68
  • [12] Mischaikow K., 2002, Handbook of Dynamical Systems. Handbook of Dynamical Systems, V2, P393
  • [13] CONNECTING ORBITS IN ONE-PARAMETER FAMILIES OF FLOWS
    REINECK, JF
    [J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1988, 8 : 359 - 374
  • [14] Hopf bifurcations in dynamical systems
    Rionero, Salvatore
    [J]. RICERCHE DI MATEMATICA, 2019, 68 (02) : 811 - 840
  • [15] SALAMON D, 1985, T AM MATH SOC, V291, P1
  • [16] Salleh Z, 2016, INT J APPL MATH STAT, V55, P122
  • [17] Using Zigzag Persistent Homology to Detect Hopf Bifurcations in Dynamical Systems
    Tymochko, Sarah
    Munch, Elizabeth
    Khasawneh, Firas A.
    [J]. ALGORITHMS, 2020, 13 (11) : 1 - 13
  • [18] Rigorous Verification of Hopf Bifurcations via Desingularization and Continuation
    van den Berg, Jan Bouwe
    Lessard, Jean-Philippe
    Queirolo, Elena
    [J]. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2021, 20 (02) : 573 - 607
  • [19] Two-parameters Hopf bifurcation in the Hodgkin-Huxley model
    Wang, J
    Geng, JM
    Fei, XY
    [J]. CHAOS SOLITONS & FRACTALS, 2005, 23 (03) : 973 - 980
  • [20] Numerical analysis of a degenerate generalized Hopf bifurcation
    Xue, Miao
    Bi, Qinsheng
    Li, Shaolong
    Xia, Yibo
    [J]. INTERNATIONAL JOURNAL OF MODERN PHYSICS C, 2021, 32 (08):
123