A density dependent delayed predator–prey model with Beddington–DeAngelis type function response incorporating a prey refuge

2015 ◽  
Vol 22 (1-3) ◽  
pp. 427-450 ◽  
Author(s):  
Jai Prakash Tripathi ◽  
Syed Abbas ◽  
Manoj Thakur
Keyword(s):  
Prey Refuge ◽  
Type Function ◽  
Predator Prey ◽  
Density Dependent ◽  
Predator Prey Model ◽  
Prey Model

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

A Predator-Prey Model Incorporating Prey Refuge and Allee Effect

2015 ◽  
Vol 713-715 ◽  
pp. 1534-1539 ◽  
Author(s):  
Rui Ning Fan
Keyword(s):  
Time Delay ◽  
Time Lag ◽  
Functional Responses ◽  
Prey Refuge ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Predator Prey Model ◽  
Prey Model ◽  
Discrete Time Delay ◽  
Prey Interaction

The effect of refuge used by prey has a stabilizing impact on population dynamics and the effect of time delay has its destabilizing influences. Little attention has been paid to the combined effects of prey refuge and time delay on the dynamic consequences of the predator-prey interaction. Here, a predator-prey model with a class of functional responses was studied by using the analytical approach. The refuge is considered as protecting a constant proportion of prey and the discrete time delay is the gestation period. We evaluated both effects with regard to the local stability of the interior equilibrium point of the considered model. The results showed that the effect of prey refuge has stronger influences than that of time delay on the considered model when the time lag is smaller than the threshold. However, if the time lag is larger than the threshold, the effect of time delay has stronger influences than that of refuge used by prey.

A note on a stochastic Holling-II predator–prey model with a prey refuge

2020 ◽  
Vol 357 (7) ◽  
pp. 4486-4502 ◽  
Author(s):  
Xiaoling Zou ◽  
Jingliang Lv ◽  
Yunpei Wu
Keyword(s):  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals Traveling Waves in a Diffusive Predator-Prey Model Incorporating a Prey Refuge

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Xiujuan Wu ◽  
Yong Luo ◽  
Yizheng Hu
Keyword(s):  
Traveling Wave ◽  
Wave Train ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Manifold Theory

We establish the existence of traveling wave solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator-prey model incorporating a prey refuge. By using the shooting argument, invariant manifold theory, and the Hopf bifurcation theorem, we analyze the dynamic behavior of this model in the three-dimensional phase space. Numerical results are also presented to illustrate the theoretical results.

The effect of prey refuge in a simple predator--prey model

2011 ◽  
Vol 222 (18) ◽  
pp. 3453-3454 ◽  
Author(s):  
Zhihui Ma ◽  
Weide Li ◽  
Shufan Wang
Keyword(s):  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model
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