scholarly journals A modified May–Holling–Tanner predator-prey model with multiple Allee effects on the prey and an alternative food source for the predator

2017 ◽  
Vol 22 (11) ◽  
pp. 0-0
Author(s):  
Claudio Arancibia-Ibarra ◽  
◽  
José Flores ◽  
Michael Bode ◽  
Graeme Pettet ◽  
...  
Keyword(s):  
Food Source ◽  
Alternative Food ◽  
Allee Effects ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Alternative Food Source

Qualitative analysis of a diffusive predator–prey model with Allee and fear effects

2021 ◽  
pp. 2150037
Author(s):  
Jia Liu
Keyword(s):  
Allee Effect ◽  
Sufficient Conditions ◽  
Allee Effects ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fear Effect ◽  
Prey Model ◽  
Strong Allee Effect ◽  
Spatially Homogeneous ◽  
Fear Effects

In this study, we consider a diffusive predator–prey model with multiple Allee effects induced by fear factors. We investigate the existence, boundedness and permanence of the solution of the system. We also discuss the existence and non-existence of non-constant solutions. We derive sufficient conditions for spatially homogeneous (non-homogenous) Hopf bifurcation and steady state bifurcation. Theoretical and numerical simulations show that strong Allee effect and fear effect have great effect on the dynamics of system.

DYNAMICS OF A DIFFUSIVE PREDATOR–PREY MODEL WITH ADDITIVE ALLEE EFFECT

2012 ◽  
Vol 05 (02) ◽  
pp. 1250023 ◽  
Author(s):  
YONGLI CAI ◽  
WEIMING WANG ◽  
JINFENG WANG
Keyword(s):  
Allee Effect ◽  
Dynamical Behavior ◽  
Positive Equilibrium ◽  
Global Asymptotical Stability ◽  
Allee Effects ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Model ◽  
Holling Ii Functional Response

In this paper, we investigate the dynamics of a diffusive predator–prey model with Holling-II functional response and the additive Allee effect in prey. We show the local and global asymptotical stability of the positive equilibrium, and give the conditions of the existence of the Hopf bifurcation. By carrying out global qualitative and bifurcation analysis, it is shown that the weak and strong Allee effects in prey can induce different dynamical behavior in the predator–prey model. Furthermore, we use some numerical simulations to illustrate the dynamics of the model. The results may be helpful for controlling and managing the predator–prey system.

scholarly journals Spatiotemporal complexity in a predator--prey model with weak Allee effects

2014 ◽  
Vol 11 (6) ◽  
pp. 1247-1274 ◽  
Author(s):  
Yongli Cai ◽  
◽  
Malay Banerjee ◽  
Yun Kang ◽  
Weiming Wang ◽  
...  
Keyword(s):  
Allee Effects ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model
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