scholarly journals Dynamics of a predator-prey system with prey subject to Allee effects and disease

2014 ◽  
Vol 11 (4) ◽  
pp. 877-918 ◽  
Author(s):  
Yun Kang ◽  
◽  
Sourav Kumar Sasmal ◽  
Amiya Ranjan Bhowmick ◽  
Joydev Chattopadhyay ◽  
...  
Keyword(s):  
Allee Effects ◽  
Predator Prey ◽  
Prey System

Cooperative hunting in a predator-prey system with Allee effects in the prey

2018 ◽  
Vol 31 (4) ◽  
pp. e12194 ◽  
Author(s):  
Sophia R.-J. Jang ◽  
Wenjing Zhang ◽  
Victoria Larriva
Keyword(s):  
Allee Effects ◽  
Predator Prey ◽  
Cooperative Hunting ◽  
Prey 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.

Dynamics of a Predator–Prey Model with Hunting Cooperation and Allee Effects in Predators

2020 ◽  
Vol 30 (14) ◽  
pp. 2050199
Author(s):  
Jun Zhang ◽  
Weinian Zhang
Keyword(s):  
Homoclinic Bifurcation ◽  
Allee Effects ◽  
Homoclinic Loop ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Analytical Parameter ◽  
Pitchfork Bifurcations ◽  
Ecosystem Diversity ◽  
Parameter Values

With both hunting cooperation and Allee effects in predators, a predator–prey system was modeled as a planar cubic differential system with three parameters. The known work numerically plots the horizontal isocline and the vertical one with appropriately chosen parameter values to show the cases of two, one and no coexisting equilibria. Transitions among those cases with the rise of limit cycle and homoclinic loop were exhibited by numerical simulations. Although it is hard to obtain the explicit expression of coordinates, in this paper, we give the distribution of equilibria qualitatively, discuss all cases of coexisting equilibria, and obtain the Bogdanov–Takens bifurcation diagram to show analytical parameter conditions for those transitions. Our results give analytical conditions for not only the observed saddle-node bifurcation, Hopf bifurcation and homoclinic bifurcation but also the transcritical and pitchfork bifurcations at the predator-extinction equilibrium, which were not considered in the known work. Our analytic conditions provide a quantitative instruction to reduce the risk of predator extinction and promote the ecosystem diversity.

scholarly journals Allee effects in a Ricker-type predator–prey system

2014 ◽  
Vol 20 (9) ◽  
pp. 1350-1371 ◽  
Author(s):  
Yunshyong Chow ◽  
Sophia R.-J. Jang
Keyword(s):  
Allee Effects ◽  
Predator Prey ◽  
Prey System

scholarly journals BIFURCATIONS OF A PREDATOR-PREY SYSTEM WITH WEAK ALLEE EFFECTS

2013 ◽  
Vol 50 (4) ◽  
pp. 695-713 ◽  
Author(s):  
Rongzhen Lin ◽  
Shengqiang Liu ◽  
Xiaohong Lai
Keyword(s):  
Allee Effects ◽  
Predator Prey ◽  
Prey System
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