Dynamics in a Predator-Prey Model with Cooperative Hunting and Allee Effect

被引：14
作者：
Du, Yanfei [1 ,2 ]
Niu, Ben [3 ]
Wei, Junjie [1 ,4 ]
机构：
[1] Harbin Inst Technol, Sch Math, Harbin 150001, Peoples R China
[2] Shaanxi Univ Sci & Technol, Sch Math & Data Sci, Xiangtan 710021, Peoples R China
[3] Harbin Inst Technol, Dept Math, Weihai 264209, Peoples R China
[4] Jimei Univ, Sch Sci, Xiamen 361021, Peoples R China
来源：
MATHEMATICS | 2021年 / 9卷 / 24期
基金：
中国国家自然科学基金;
关键词：
hunting cooperation; Allee effect; connecting orbit; invariant manifold; bifurcation; coexistence; DELAY-DIFFERENTIAL EQUATIONS; TURING-HOPF BIFURCATION; QUALITATIVE-ANALYSIS; TIME-DELAY; PACK SIZE; STABILITY; SYSTEM; MEMORY;
D O I：
10.3390/math9243193
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper deals with a diffusive predator-prey model with two delays. First, we consider the local bifurcation and global dynamical behavior of the kinetic system, which is a predator-prey model with cooperative hunting and Allee effect. For the model with weak cooperation, we prove the existence of limit cycle, and a loop of heteroclinic orbits connecting two equilibria at a threshold of conversion rate p=p#, by investigating stable and unstable manifolds of saddles. When p > p#, both species go extinct, and when p
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页数：40
相关论文
共 74 条
[1]   Nonintegrability of the unfoldings of codimension-two bifurcations [J].
Acosta-Humanezi, Primitivo B. ;
Yagasaki, Kazuyuki .
NONLINEARITY, 2020, 33 (04) :1366-1387
[2]   GLOBAL BIFURCATIONS OF PERIODIC ORBITS [J].
ALEXANDER, JC ;
YORKE, JA .
AMERICAN JOURNAL OF MATHEMATICS, 1978, 100 (02) :263-292
[3]   Hunting cooperation and Allee effects in predators [J].
Alves, Mickael Teixeira ;
Hilker, Frank M. .
JOURNAL OF THEORETICAL BIOLOGY, 2017, 419 :13-22
[4]   SPATIOTEMPORAL ATTRACTORS GENERATED BY THE TURING-HOPF BIFURCATION IN A TIME-DELAYED REACTION-DIFFUSION SYSTEM [J].
An, Qi ;
Jiang, Weihua .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2019, 24 (02) :487-510
[5]  
[Anonymous], 1992, STABILITY OSCILLATIO
[6]  
[Anonymous], 1938, The Social Life of Animals
[7]   Impacts of Foraging Facilitation Among Predators on Predator-prey Dynamics [J].
Berec, Ludek .
BULLETIN OF MATHEMATICAL BIOLOGY, 2010, 72 (01) :94-121
[8]   COOPERATIVE HUNTING IN WILD CHIMPANZEES [J].
BOESCH, C .
ANIMAL BEHAVIOUR, 1994, 48 (03) :653-667
[9]   Interspecific communicative and coordinated hunting between groupers and giant moray eels in the Red Sea [J].
Bshary, Redouan ;
Hohner, Andrea ;
Ait-el-Djoudi, Karim ;
Fricke, Hans .
PLOS BIOLOGY, 2006, 4 (12) :2393-2398
[10]  
Campbell S.A., 1995, J. Dyn. Diff. Eq, V7, P213, DOI DOI 10.1007/BF02218819
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