Dynamic analysis of a fractional order delayed predator-prey system with harvesting

被引：34

作者：

Song, Ping ^{[1
]}

Zhao, Hongyong ^{[1
]}

Zhang, Xuebing ^{[1
,2
]}

机构：

[1] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 210016, Jiangsu, Peoples R China

[2] Huaian Coll Informat Technol, Dept Basic Course, Huaian 223003, Peoples R China

来源：

THEORY IN BIOSCIENCES | 2016年 / 135卷 / 1-2期

基金：

中国国家自然科学基金;

关键词：

Predator-prey system; Time delay; Harvesting; Stability; Fractional derivative; HOPF-BIFURCATION; STAGE STRUCTURE; TIME-DELAY; MODEL; STABILITY;

D O I：

10.1007/s12064-016-0223-0

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In the study, we consider a fractional order delayed predator-prey system with harvesting terms. Our discussion is divided into two cases. Without harvesting, we investigate the stability of the model, as well as deriving some criteria by analyzing the associated characteristic equation. With harvesting, we investigate the dynamics of the system from the aspect of local stability and analyze the influence of harvesting to prey and predator. Finally, numerical simulations are presented to verify our theoretical results. In addition, using numerical simulations, we investigate the effects of fractional order and harvesting terms on dynamic behavior. Our numerical results show that fractional order can affect not only the stability of the system without harvesting terms, but also the switching times from stability to instability and to stability. The harvesting can convert the equilibrium point, the stability and the stability switching times.

引用

页码：59 / 72

页数：14

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