STABILITY AND HOPF BIFURCATION ANALYSIS ON A SPRUCE-BUDWORM MODEL WITH DELAY

被引：1

作者：

Zhang, Lijun ^{[1
]}

Zhang, Jianming ^{[2
]}

机构：

[1] Shandong Univ Sci & Technol Qingdao, Coll Math & Syst Sci, Qingdao 266590, Shandong, Peoples R China

[2] Zhejiang Sci Tech Univ, Sch Sci, Dept Math, Hangzhou 310018, Zhejiang, Peoples R China

来源：

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2020年 / 10卷 / 06期

关键词：

Spruce-budworm; Hopf bifurcation; normal form; center manifold; PREDATOR-PREY MODEL; RELAXATION OSCILLATIONS; SPATIOTEMPORAL DYNAMICS; FLUID;

D O I：

10.11948/20200084

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the dynamics of a spruce-budworm model with delay is investigated. We show that there exists Hopf bifurcation at the positive equilibrium as the delay increases. Some sufficient conditions for the existence of Hopf bifurcation are obtained by investigating the associated characteristic equation. By using the theory of normal form and center manifold, explicit expression for determining the direction of Hopf bifurcations and the stability of bifurcating periodic solutions are presented.

引用

页码：2711 / 2721

页数：11

共 21 条

[1] Supercritical and subcritical Hopf-bifurcations in a two-delayed prey-predator system with density-dependent mortality of predator and strong Allee effect in prey [J].

Banerjee, Jeet ;

Sasmal, Sourav Kumar ;

Layek, Ritwik Kumar .

BIOSYSTEMS, 2019, 180 :19-37

[2] BOGDANOV-TAKENS BIFURCATION IN A DELAYED MICHAELIS-MENTEN TYPE RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH PREY HARVESTING [J].

Dai, Yunxian ;

Yang, Ping ;

Luo, Zhiliang ;

Lin, Yiping .

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2019, 9 (04) :1333-1346

[3] Nonlinear vibration isolation for fluid-conveying pipes using quasi-zero stiffness characteristics [J].

Ding, Hu ;

Ji, Jinchen ;

Chen, Li-Qun .

MECHANICAL SYSTEMS AND SIGNAL PROCESSING, 2019, 121 :675-688

[4] EFFECT OF HERD SHAPE IN A DIFFUSIVE PREDATOR-PREY MODEL WITH TIME DELAY [J].

Djilali, Salih .

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2019, 9 (02) :638-654

[5]

Hassard B.D., 1981, Theory and Applications of Hopf Bifurcation

[6]

Holling C. S., 1959, Canadian Entomologist, V91, P385

[7] Impact of Allee effect on an eco-epidemiological system [J].

Kumar, Udai ;

Mandal, Partha Sarathi ;

Venturino, E. .

ECOLOGICAL COMPLEXITY, 2020, 42

[8] Relaxation oscillations in a class of predator-prey systems [J].

Liu, WS ;

Xiao, DM ;

Yi, YF .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2003, 188 (01) :306-331

[9] QUALITATIVE-ANALYSIS OF INSECT OUTBREAK SYSTEMS - SPRUCE BUDWORM AND FOREST [J].

LUDWIG, D ;

JONES, DD ;

HOLLING, CS .

JOURNAL OF ANIMAL ECOLOGY, 1978, 47 (01) :315-332

[10] Allee effect acting on the prey species in a Leslie-Gower predation model [J].

Martinez-Jeraldo, Nicole ;

Aguirre, Pablo .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2019, 45 :895-917

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