HOPF-FOLD BIFURCATION AND FLUCTUATION PHENOMENA IN A DELAYED RATIO-DEPENDENT GAUSE-TYPE PREDATOR-PREY MODEL

被引：1
|
作者：
Guo, Shuang [2 ]
Jiang, Weihua [1 ]
机构：
[1] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
[2] Daqing Normal Univ, Sch Math Sci, Daqing 163712, Peoples R China
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2013年 / 23卷 / 09期
基金：
中国国家自然科学基金;
关键词：
Gause-type model; Hopf-Fold bifurcation; fluctuation; quasi-periodic; bursting behavior; DIFFERENTIAL EQUATIONS; TIME-DELAY; DYNAMICS; SYSTEM; SYNCHRONIZATION; NEURONS;
D O I：
10.1142/S0218127413501538
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A class of delayed ratio-dependent Gause-type predator-prey model is considered. We study the eigenvalue problem for the linearized system at the coexisting equilibrium. For a critical case when the characteristic equation has a single zero root and a simple pair of pure imaginary roots, a complete bifurcation analysis is presented by employing the center manifold reduction and the normal form method. We analyzed the influence of the time delay on the Hopf-Fold bifurcation and showed the occurrence of quasi-periodic motion and bursting behavior. This phenomenon is in line with the seasonal variation law of the population.
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页数：20
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