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

被引：20

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 41 条

[1]

Agarwal R., 2014, Oscillation and Stability of Delay Models in Biology

[2]

[Anonymous], 1991, THEORY APPL PARTIAL

[3] MUTUAL INTERFERENCE BETWEEN PARASITES OR PREDATORS AND ITS EFFECT ON SEARCHING EFFICIENCY [J].

BEDDINGTON, JR .

JOURNAL OF ANIMAL ECOLOGY, 1975, 44 (01) :331-340

[4] Dynamic behaviors of a non-selective harvesting Lotka-Volterra amensalism model incorporating partial closure for the populations [J].

Chen, Baoguo .

ADVANCES IN DIFFERENCE EQUATIONS, 2018,

[5]

Chen F., 2015, J. Beihua. Univ, V16, P141, DOI DOI 10.1007/s11859-015-1072-2

[6]

Chen F., 2015, Journal of Shengyang University(Natural Science), V27, P251, DOI 10.1080/17513750802560346

[7] Stability and Bifurcation in a Diffusive Logistic Population Model with Multiple Delays [J].

Chen, Shanshan ;

Wei, Junjie .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2015, 25 (08)

[8] MODEL FOR TROPHIC INTERACTION [J].

DEANGELIS, DL ;

GOLDSTEIN, RA ;

ONEILL, RV .

ECOLOGY, 1975, 56 (04) :881-892

[9] Dynamical analysis of a two species amensalism model with Beddington-DeAngelis functional response and Allee effect on the second species [J].

Guan, Xinyu ;

Chen, Fengde .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2019, 48 :71-93

[10]

Hale JK., 1977, Theory of Functional Differential Equations, DOI 10.1007/978-1-4612-9892-2

← 1 2 3 4 5 →