Global analysis of a Holling type II predator–prey model with a constant prey refuge

2013 ◽  
Vol 76 (1) ◽  
pp. 635-647 ◽  
Author(s):  
Guangyao Tang ◽  
Sanyi Tang ◽  
Robert A. Cheke
Keyword(s):  
Global Analysis ◽  
Type Ii ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals Permanence and global attractivity of a nonautonomous modified Leslie-Gower predator-prey model with Holling-type II schemes and a prey refuge

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Xiangdong Xie ◽  
Yalong Xue ◽  
Jinhuang Chen ◽  
Tingting Li
Keyword(s):  
Global Attractivity ◽  
Type Ii ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals Dynamical Analysis Predator-Prey Population with Holling Type II Functional Response

2021 ◽  
Author(s):  
FE. Universitas Andi Djemma
Keyword(s):  
Functional Response ◽  
Equilibrium Points ◽  
Dynamical Analysis ◽  
Type Ii ◽  
Asymptotically Stable ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Type Ii Functional Response

In this article, we investigate the dynamical analysis of predator prey model. Interactionamong preys and predators use Holling type II functional response, and assuming prey refuge aswell as harvesting in both populations. This study aims to study the predator prey model and todetermine the effect of overharvesting which consequently will affect the ecosystem. In the modelfound three equilibrium points, i.e., (0,0) is the extinction of predator and prey equilibrium,?(??, 0) is the equilibrium with predatory populations extinct and the last equilibrium points?(??, ??) is the coexist equilibrium. All equilibrium points are asymptotically stable (locally) undercertain conditions. These analytical findings were confirmed by several numerical simulations.

GLOBAL ANALYSIS OF A HARVESTED PREDATOR–PREY MODEL INCORPORATING A CONSTANT PREY REFUGE

2010 ◽  
Vol 03 (02) ◽  
pp. 205-223 ◽  
Author(s):  
LIUJUAN CHEN ◽  
FENGDE CHEN
Keyword(s):  
Prey Species ◽  
Global Analysis ◽  
Sufficient Conditions ◽  
Equilibrium Density ◽  
Prey Refuge ◽  
Predator Species ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Density Values

A predator–prey model with Holling type II functional response incorporating a constant prey refuge and independent harvesting in either species is investigated. Some sufficient conditions of the instability and stability properties to the equilibria and the existence and uniqueness to limit cycles for the model are obtained. We also show that influence of prey refuge and harvesting efforts on equilibrium density values. One of the surprising finding is that for fixed prey refuge, harvesting has no influence on the final density of the prey species, while the density of predator species is decreasing with the increasing of harvesting effort on prey species and the fixation of harvesting effort on predator species. Numerical simulations are carried out to illustrate the obtained results and the dependence of the dynamic behavior on the harvesting efforts or prey refuge.

scholarly journals Global analysis of a predator–prey model with variable predator search rate

2020 ◽  
Vol 81 (1) ◽  
pp. 159-183 ◽  
Author(s):  
Benjamin D. Dalziel ◽  
Enrique Thomann ◽  
Jan Medlock ◽  
Patrick De Leenheer
Keyword(s):  
Global Analysis ◽  
Search Rate ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

Dynamic behaviors of a Lotka–Volterra predator–prey model incorporating a prey refuge and predator mutual interference

2013 ◽  
Vol 219 (15) ◽  
pp. 7945-7953 ◽  
Author(s):  
Zhaozhi Ma ◽  
Fengde Chen ◽  
Chengqiang Wu ◽  
Wanlin Chen
Keyword(s):  
Mutual Interference ◽  
Prey Refuge ◽  
Dynamic Behaviors ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals Dynamic behaviors of a nonautonomous predator–prey system with Holling type II schemes and a prey refuge

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yumin Wu ◽  
Fengde Chen ◽  
Caifeng Du
Keyword(s):  
Lyapunov Function ◽  
Differential Equations ◽  
Comparison Theorem ◽  
Sufficient Conditions ◽  
Oscillation Theory ◽  
Type Ii ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System

AbstractIn this paper, we consider a nonautonomous predator–prey model with Holling type II schemes and a prey refuge. By applying the comparison theorem of differential equations and constructing a suitable Lyapunov function, sufficient conditions that guarantee the permanence and global stability of the system are obtained. By applying the oscillation theory and the comparison theorem of differential equations, a set of sufficient conditions that guarantee the extinction of the predator of the system is obtained.

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