Bifurcation analysis in a discrete differential-algebraic predator-prey system

被引：28
作者：
Zhang, Guodong [1 ,2 ]
Shen, Yi [1 ,2 ]
Chen, Boshan [3 ]
机构：
[1] Huazhong Univ Sci & Technol, Sch Automat, Wuhan 430074, Peoples R China
[2] Huazhong Univ Sci & Technol, Key Lab Minist Educ Image Proc & Intelligent Cont, Wuhan 430074, Peoples R China
[3] Hubei Normal Univ, Coll Math & Stat, Huangshi 435002, Peoples R China
来源：
APPLIED MATHEMATICAL MODELLING | 2014年 / 38卷 / 19-20期
基金：
中国国家自然科学基金; 美国国家科学基金会;
关键词：
Bifurcation; Stability; Chaos; Discrete differential-algebraic system; Predator-prey; STAGE-STRUCTURE; MODEL; BEHAVIOR;
D O I：
10.1016/j.apm.2014.03.042
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
The discrete-time predator-prey biological economic system obtained by Euler method is investigated. Some conditions for the system to undergo flip bifurcation and Neimark-Sacker bifurcation are derived by using new normal form of differential-algebraic system, center mainfold theorem and bifurcation theory. Numerical simulations are given to show the effectiveness of our results and also to exhibit period-doubling bifurcation in orbits of period 2, 4, 8 and chaotic sets. The results obtained here reveal far richer dynamics in discrete differential-algebraic biological economic system. The contents are interesting in mathematics and biology. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：4835 / 4848
页数：14
相关论文
共 27 条
[11]   Bifurcation and chaotic behavior of a discrete-time predator-prey system [J].
He, Zhimin ;
Lai, Xin .
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2011, 12 (01) :403-417
[12]  
Holling C. S., 1965, Mem ent Soc Canada Ottawa, Vno. 45, P1
[13]   Stability and bifurcation analysis of a discrete predator-prey model with nonmonotonic functional response [J].
Hu, Zengyun ;
Teng, Zhidong ;
Zhang, Long .
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2011, 12 (04) :2356-2377
[14]   Modelling and analysis of a prey-predator system with stage-structure and harvesting [J].
Kar, T. K. ;
Pahari, U. K. .
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2007, 8 (02) :601-609
[15]  
Kar TK, 2006, J COMPUT APPL MATH, V185, P19, DOI [10.1016/j.cam.2005.01.035, 10.1016/j.cam.20050.01.035]
[16]   THE PROPERTIES OF A STOCHASTIC MODEL FOR THE PREDATOR-PREY TYPE OF INTERACTION BETWEEN 2 SPECIES [J].
LESLIE, PH ;
GOWER, JC .
BIOMETRIKA, 1960, 47 (3-4) :219-234
[17]   Stability and Hopf bifurcation analysis of a prey-predator system with two delays [J].
Li, Kai ;
Wei, Junjie .
CHAOS SOLITONS & FRACTALS, 2009, 42 (05) :2606-2613
[18]   Dynamical behavior in a stage-structured differential-algebraic prey-predator model with discrete time delay and harvesting [J].
Liu, Chao ;
Zhang, Qingling ;
Zhang, Xue ;
Duan, Xiaodong .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 231 (02) :612-625
[19]   Complex dynamic behaviors of a discrete-time predator-prey system [J].
Liu, Xiaoli ;
Xiao, Dongmei .
CHAOS SOLITONS & FRACTALS, 2007, 32 (01) :80-94
[20]   Bifurcation analysis in a predator-prey system with time delay [J].
Song, YL ;
Yuan, SL .
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2006, 7 (02) :265-284
123