Hopf Bifurcation Analysis of a Housefly Model with Time Delay

被引：1

作者：

Chang, Xiaoyuan ^{[1
]}

Gao, Xu ^{[1
]}

Zhang, Jimin ^{[2
]}

机构：

[1] Harbin Univ Sci & Technol, Sch Sci, Harbin 150080, Heilongjiang, Peoples R China

[2] Heilongjiang Univ, Sch Math Sci, Harbin 150080, Heilongjiang, Peoples R China

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2023年 / 33卷 / 09期

关键词：

Supercritical Hopf bifurcation; global stability; time delay; the housefly model; transient oscillation; POPULATION-MODELS; STABILITY; RESISTANT; SYSTEM;

D O I：

10.1142/S0218127423501067

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The oscillatory dynamics of a delayed housefly model is analyzed in this paper. The local and global stabilities at the non-negative equilibria are obtained via analyzing the distribution of eigenvalues and Lyapunov-LaSalle invariance principle, and the model undergoes the supercritical Hopf bifurcation and the transient oscillation. Based on Wu's global Hopf bifurcation theory, the existence of the global bifurcation is established under certain conditions.

引用

页数：11

共 33 条

[1] INSTABILITY AND COMPLEX DYNAMIC BEHAVIOR IN POPULATION-MODELS WITH LONG-TIME DELAYS [J].

BLYTHE, SP ;

NISBET, RM ;

GURNEY, WSC .

THEORETICAL POPULATION BIOLOGY, 1982, 22 (02) :147-176

[2] RESISTANCE OF HOUSEFLIES TO GAMMA-BENZENE HEXACHLORIDE AND DIELDRIN [J].

BRIDGES, RG ;

COX, JT .

NATURE, 1959, 184 (4700) :1740-1741

[3] Dynamics of a Scalar Population Model with Delayed Allee Effect [J].

Chang, Xiaoyuan ;

Shi, Junping ;

Zhang, Jimin .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2018, 28 (12)

[4] Global dynamics of the diffusive Lotka-Volterra competition model with stage structure [J].

Chen, Shanshan ;

Shi, Junping .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2020, 59 (01)

[5] Stability and Hopf bifurcation in a diffusive logistic population model with nonlocal delay effect [J].

Chen, Shanshan ;

Shi, Junping .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 253 (12) :3440-3470

[6]

Coppel W.A., 1965, Stability and asymptotic behavior of differential equations

[7] A delay-differential equation model of HIV infection of CD4+ T-cells [J].

Culshaw, RV ;

Ruan, SG .

MATHEMATICAL BIOSCIENCES, 2000, 165 (01) :27-39

[8]

Deng WH, 2007, NONLINEAR DYNAM, V48, P409, DOI [10.1007/s11071-006-9094-0, 10.1007/s11071 -006-9094-0]

[9]

FIEDLER M, 1974, CZECH MATH J, V24, P392

[10]

Hale JK, 2013, Introduction to functional differential equations, V99

← 1 2 3 4 →