Complex dynamics of ecological systems under nonlinear harvesting: Hopf bifurcation and Turing instability

被引：31
|
作者：
Upadhyay, Ranjit Kumar [1 ]
Roy, Parimita [1 ]
Datta, Jyotiska [2 ]
机构：
[1] Indian Sch Mines, Dept Appl Math, Dhanbad 826004, Bihar, India
[2] Cent Univ Orissa, Ctr Math, Koraput 764020, Odisha, India
来源：
NONLINEAR DYNAMICS | 2015年 / 79卷 / 04期
关键词：
Turing instability; Pattern formation; Hopf bifurcation; Harvesting; Holling type IV functional response; PREDATOR-PREY MODEL; SPATIAL-PATTERN FORMATION;
D O I：
10.1007/s11071-014-1808-0
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
In this paper, we study the complex dynamics of a spatial nonlinear predator-prey system under harvesting. A modified Leslie-Gower model with Holling type IV functional response and nonlinear harvesting of prey is considered. We perform a detailed stability and Hopf bifurcation analysis of the spatial model system and determine the direction of Hopf bifurcation and stability of the bifurcating periodic solutions. Numerical simulations were performed to figure out how Turing patterns evolve under nonlinear harvesting. Simulation study leads to a few interesting sequences of pattern formation, which may be relevant in real world situations.
引用
收藏
页码：2251 / 2270
页数：20
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