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.

引用

页码：216 / 224

页数：9

共 21 条

[1] Conley C., 1978, Isolated invariant sets and the Morse index, V38
[2] Transient behavior towards the stable limit cycle in the Sel'kov model of Glycolysis: A physiological disorder'
Das, Tanmay
Acharyya, Muktish
[J]. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2021, 567 (567)
[3] INDEX FILTRATIONS AND THE HOMOLOGY INDEX BRAID FOR PARTIALLY ORDERED MORSE DECOMPOSITIONS
FRANZOSA, R
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 298 (01) : 193 - 213
[4] THE CONNECTION MATRIX-THEORY FOR MORSE DECOMPOSITIONS
FRANZOSA, RD
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1989, 311 (02) : 561 - 592
[5] THE CONTINUATION THEORY FOR MORSE DECOMPOSITIONS AND CONNECTION MATRICES
FRANZOSA, RD
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 310 (02) : 781 - 803
[6] [GUO Gaihui 郭改慧], 2011, [应用数学, Mathematics Applicata], V24, P467
[7] Hatcher A, 2002, Algebraic Topology
[8] Global Hopf Bifurcation for Differential-Algebraic Equations with State-Dependent Delay
Hu, Qingwen
[J]. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2019, 31 (01) : 93 - 128
[9] HOMOTOPY INVARIANTS OF REPELLER-ATTRACTOR PAIRS .1. THE PUPPE SEQUENCE OF AN R-A PAIR
KURLAND, HL
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1982, 46 (01) : 1 - 31
[10] Stability and Hopf bifurcation analysis in a Lotka-Volterra competition-diffusion-advection model with time delay effect
Li, Zhenzhen
Dai, Binxiang
[J]. NONLINEARITY, 2021, 34 (05) : 3271 - 3313

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