Stability and Hopf Bifurcation Analysis for a Two-Species Commensalism System with Delay

被引：17

作者：

Li, Tianyang ^{[1
]}

Wang, Qiru ^{[1
]}

机构：

[1] Sun Yat Sen Univ, Sch Math, Guangzhou 510275, Guangdong, Peoples R China

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2021年 / 20卷 / 03期

基金：

中国国家自然科学基金;

关键词：

A two-species commensalism system; Time delay; Stability; Hopf bifurcation; DIFFERENTIAL EQUATIONS; PERIODIC-SOLUTIONS; AMENSALISM MODEL;

D O I：

10.1007/s12346-021-00524-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to studying the dynamics of a two-species commensalism system with delay. By analyzing the characteristic equation and regarding the time delay as the bifurcation parameter, we investigate the local asymptotic stability of the positive equilibrium and show the existence of periodic solutions bifurcating from the positive equilibrium. Then, we derive the precise formulae to determine the Hopf bifurcation direction and the stability of the bifurcating periodic solutions by using the normal form theory and the center manifold theorem. Numerical simulation results are also included to support our theoretical analysis.

引用

页数：20

共 50 条

[1] Stability and Hopf Bifurcation Analysis for a Two-Species Commensalism System with Delay
Tianyang Li
Qiru Wang
Qualitative Theory of Dynamical Systems, 2021, 20
[2] Bifurcation Analysis for Two-Species Commensalism (Amensalism) Systems with Distributed Delays
Li, Tianyang
Wang, Qiru
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2022, 32 (09):
[3] Stability and Hopf Bifurcation in a Two-species Fishery Model with Selective Harvesting
Ma, Jian
Zheng, Baodong
Zhang, Chunrui
PROCEEDINGS OF THE 7TH CONFERENCE ON BIOLOGICAL DYNAMIC SYSTEM AND STABILITY OF DIFFERENTIAL EQUATION, VOLS I AND II, 2010, : 220 - 227
[4] Stochastic Hopf–Hopf bifurcation of two-species discrete coupling logistic system with symbiotic interaction
Maosong Yang
Shaojuan Ma
Advances in Difference Equations, 2020
[5] HOPF BIFURCATION IN A TWO-SPECIES REACTION-DIFFUSION-ADVECTION COMPETITIVE MODEL WITH NONLOCAL DELAY
Wen, Tingting
Wang, Xiaoli
Zhang, Guohong
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2023, 22 (05) : 1517 - 1544
[6] Hopf bifurcation in a reaction-diffusive-advection two-species competition model with one delay
Meng, Qiong
Liu, Guirong
Jin, Zhen
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2021, (72) : 1 - 24
[7] Stability analysis and Hopf bifurcation for two-species reaction-diffusion-advection competition systems with two time delays
Alfifi, H. Y.
APPLIED MATHEMATICS AND COMPUTATION, 2024, 474
[8] Stochastic Hopf-Hopf bifurcation of two-species discrete coupling logistic system with symbiotic interaction
Yang, Maosong
Ma, Shaojuan
ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)
[9] Hopf bifurcation in a reaction-diffusive two-species model with nonlocal delay effect and general functional response
Han, Renji
Dai, Binxiang
CHAOS SOLITONS & FRACTALS, 2017, 96 : 90 - 109
[10] Stability and Hopf bifurcation for a delay competition diffusion system
Zhou, L
Tang, YB
Hussein, SG
CHAOS SOLITONS & FRACTALS, 2002, 14 (08) : 1201 - 1225

← 1 2 3 4 5 →