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
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