Modeling the Effect of Prey Refuge on a Ratio-Dependent Predator–Prey System with the Allee Effect

2018 ◽  
Vol 80 (3) ◽  
pp. 626-656 ◽  
Author(s):  
Maitri Verma ◽  
A. K. Misra
Keyword(s):  
Allee Effect ◽  
Prey Refuge ◽  
Predator Prey ◽  
Prey System ◽  
Ratio Dependent

NONCONSTANT PREY HARVESTING IN RATIO-DEPENDENT PREDATOR–PREY SYSTEM INCORPORATING A CONSTANT PREY REFUGE

2012 ◽  
Vol 05 (02) ◽  
pp. 1250021 ◽  
Author(s):  
SAPNA DEVI
Keyword(s):  
Rate Function ◽  
Predator Population ◽  
Catch Per Unit Effort ◽  
Prey Refuge ◽  
Predator Prey ◽  
Prey System ◽  
Optimal Harvest ◽  
Ratio Dependent ◽  
The Stability ◽  
Optimal Harvest Policy

This paper deals with the problem of nonconstant harvesting of prey in a ratio-dependent predator–prey system incorporating a constant prey refuge. Here we use the reasonable catch-rate function instead of usual catch-per-unit-effort hypothesis. The existence, as well as the stability of possible equilibria, is carried out. Bionomic equilibrium of the system is determined and optimal harvest policy is studied with the help of Pontryagin's maximum principle. The key results developed in this paper are illustrated using numerical simulations. Our results indicate that dynamic behavior of the system very much depends on the prey refuge parameter and increasing amount of refuge could increase prey density and may lead to the extinction of predator population density.

Impact of Prey Refuge on a Discrete Time Predator–Prey System with Allee Effect

2014 ◽  
Vol 24 (09) ◽  
pp. 1450106 ◽  
Author(s):  
Sourav Rana ◽  
Amiya Ranjan Bhowmick ◽  
Sabyasachi Bhattacharya
Keyword(s):  
Discrete Time ◽  
Allee Effect ◽  
Chaotic Behavior ◽  
Large Fraction ◽  
Chaotic Oscillation ◽  
Prey Refuge ◽  
Predator Prey ◽  
Prey System ◽  
The Stability ◽  
The Impact

We study the impact of the Allee effect and prey refuge on the stability of a discrete time predator–prey system. We focus on the stability behavior of the system with the Allee effect in predator, prey and both populations. Based on the combination of analytical and numerical results, we observe that: (1) the Allee effect stabilizes the systems dynamics in a moderate value of prey refuge. (2) For a large fraction of prey refuge no significant improvement in stability is observed due to Allee effect. (3) Refuge may play an important role in managing the populations which are subject to the Allee effect. The population remains stable at an intermediate level of refuge parameter, whereas at relatively low and high refuge effect, prey exhibits chaotic oscillation. Such chaotic behavior is suppressed in the presence of Allee effect. The Allee mechanism and refuge are considered simultaneously on the populations and is shown to have a significant impact on the predator–prey dynamics that may be helpful in the conservation of endangered species.

scholarly journals Complex Dynamical Behavior of a Predator-Prey System with Group Defense

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Jianglin Zhao ◽  
Min Zhao ◽  
Hengguo Yu
Keyword(s):  
Numerical Simulation ◽  
Theoretical Basis ◽  
Dynamical Behavior ◽  
Turing Instability ◽  
Equilibrium Density ◽  
Prey Refuge ◽  
Predator Prey ◽  
Prey System ◽  
Group Defense ◽  
Complex Dynamical Behavior

A diffusive predator-prey system with prey refuge is studied analytically and numerically. The Turing bifurcation is analyzed in detail, which in turn provides a theoretical basis for the numerical simulation. The influence of prey refuge and group defense on the equilibrium density and patterns of species under the condition of Turing instability is explored by numerical simulations, and this shows that the prey refuge and group defense have an important effect on the equilibrium density and patterns of species. Moreover, it can be obtained that the distributions of species are more sensitive to group defense than prey refuge. These results are expected to be of significance in exploration for the spatiotemporal dynamics of ecosystems.

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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