scholarly journals The existence, bifurcation and stability of positive stationary solutions of a diffusive Leslie–Gower predator–prey model with Holling-type II functional responses

2013 ◽  
Vol 405 (2) ◽  
pp. 618-630 ◽  
Author(s):  
Jun Zhou ◽  
Junping Shi
Keyword(s):  
Stationary Solutions ◽  
Type Ii ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Bifurcation And Stability

scholarly journals Dynamics Analysis of a Stochastic Leslie–Gower Predator-Prey Model with Feedback Controls

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Huailan Ren ◽  
Wencai Zhao
Keyword(s):  
Lyapunov Functions ◽  
Type Ii ◽  
Functional Responses ◽  
Feedback Controls ◽  
Predator Prey ◽  
Noise Interference ◽  
Predator Prey Model ◽  
Prey Model ◽  
Global Positive Solution ◽  
Theoretical Results

This study focuses on the investigation of a stochastic Leslie–Gower predator-prey model with feedback controls and Holling type II functional responses. First, the existence and uniqueness of a global positive solution to the system under white noise interference are proved. Second, the conditions for the existence of the system’s positive recurrence are established by constructing suitable Lyapunov functions. Additionally, the persistence and extinction of prey and predator in the system are discussed, and the impacts of noise interference and feedback controls on the system are revealed. Finally, we validate the theoretical results by numerical simulations.

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

GLOBAL STABILITY OF A STAGE-STRUCTURED PREDATOR–PREY MODEL WITH MODIFIED LESLIE–GOWER AND HOLLING-TYPE II SCHEMES

2012 ◽  
Vol 05 (06) ◽  
pp. 1250057 ◽  
Author(s):  
ZHONG LI ◽  
MAOAN HAN ◽  
FENGDE CHEN
Keyword(s):  
Global Stability ◽  
Positive Equilibrium ◽  
Type Ii ◽  
Iterative Technique ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

In this paper, we consider a stage-structured predator–prey model with modified Leslie–Gower and Holling-type II schemes. Using an iterative technique, we investigate the global stability of the positive equilibrium of the system. Finally, some examples are presented to verify our main result.

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.

Analysis of a Stochastic Holling Type II Predator–Prey Model Under Regime Switching

2019 ◽  
Vol 43 (3) ◽  
pp. 2171-2197
Author(s):  
Xiaobo Jiang ◽  
Li Zu ◽  
Daqing Jiang ◽  
Donal O’Regan
Keyword(s):  
Regime Switching ◽  
Type Ii ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

Dynamics of a stochastic Holling type II predator–prey model with hyperbolic mortality

2016 ◽  
Vol 87 (3) ◽  
pp. 2011-2020 ◽  
Author(s):  
Xinhong Zhang ◽  
Yan Li ◽  
Daqing Jiang
Keyword(s):  
Type Ii ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model
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