Dynamical properties of a prey-predator-scavenger model with quadratic harvesting

被引：34

作者：

Gupta, R. P. ^{[1
]}

Chandra, Peeyush ^{[2
,3
]}

机构：

[1] Banaras Hindu Univ, Inst Sci, Dept Math, Varanasi 221005, Uttar Pradesh, India

[2] Vicenza Highbreeze, B603,Kalali Link Rd, Vadodara 390012, India

[3] Indian Inst Technol Kanpur, Dept Math & Stat, Kanpur 208016, Uttar Pradesh, India

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2017年 / 49卷

关键词：

Prey-predator-scavenger model; Stability and Hopf-bifurcation; Period doubling route to chaos; Optimal control; PERIOD-DOUBLING BIFURCATIONS; HOMOCLINIC BIFURCATIONS; CHAOS; CASCADES; SYSTEM; ROUTE;

D O I：

10.1016/j.cnsns.2017.01.026

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose and analyze an extended model for the prey-predator-scavenger in presence of harvesting to study the effects of harvesting of predator as well as scavenger. The positivity, boundedness and persistence conditions are derived for the proposed model. The model undergoes a Hopf-bifurcation around the co-existing equilibrium point. It is also observed that the model is capable of exhibiting period doubling route to chaos. It is pointed out that a suitable amount of harvesting of predator can control the chaotic dynamics and make the system stable. An extensive numerical simulation is performed to validate the analytic findings. The associated control problem for the proposed model has been analyzed for optimal harvesting. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：202 / 214

页数：13

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