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

scholarly journals Cooperative hunting in a discrete predator–prey system II

2018 ◽  
Vol 13 (sup1) ◽  
pp. 247-264 ◽  
Author(s):  
Yunshyong Chow ◽  
Sophia R.-J. Jang ◽  
Hua-Ming Wang
Keyword(s):  
Predator Prey ◽  
Cooperative Hunting ◽  
Prey System

scholarly journals Cooperative hunting in a discrete predator–prey system

2020 ◽  
Vol 13 (07) ◽  
pp. 2050063
Author(s):  
Yunshyong Chow ◽  
Sophia R.-J. Jang ◽  
Hua-Ming Wang
Keyword(s):  
Growth Rate ◽  
Discrete Time ◽  
Reproductive Number ◽  
Model Parameters ◽  
Predator Population ◽  
Sufficient Condition ◽  
Predator Prey ◽  
Cooperative Hunting ◽  
Prey System ◽  
Dependent Growth

We propose and investigate a discrete-time predator–prey system with cooperative hunting in the predator population. The model is constructed from the classical Nicholson–Bailey host-parasitoid system with density dependent growth rate. A sufficient condition based on the model parameters for which both populations can coexist is derived, namely that the predator’s maximal reproductive number exceeds one. We study existence of interior steady states and their stability in certain parameter regimes. It is shown that the system behaves asymptotically similar to the model with no cooperative hunting if the degree of cooperation is small. Large cooperative hunting, however, may promote persistence of the predator for which the predator would otherwise go extinct if there were no cooperation.

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 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

scholarly journals Bifurcations of a predator-prey system with cooperative hunting and Holling III functional response

2021 ◽  
Author(s):  
Yong Yao ◽  
Teng Song ◽  
Zuxiong Li
Keyword(s):  
Functional Response ◽  
Positive Equilibrium ◽  
Predator Prey ◽  
Weak Focus ◽  
Cooperative Hunting ◽  
Prey System ◽  
Saddle Node ◽  
Boundary Equilibrium ◽  
Parameter Values ◽  
Holling Iii Functional Response

Abstract In this paper, we consider the dynamics of a predator-prey system of Gause type with cooperative hunting among predators and Holling III functional response. The known work numerically shows that the system exhibits saddle-node and Hopf bifurcations except homoclinic bifurcation for some special parameter values. Our results show that there are a weak focus of multiplicity three and a cusp of codimension two for general parameter conditions and the system can exhibit various bifurcations as perturbing the bifurcation parameters appropriately, such as the transcritical and the pitchfork bifurcations at the degenerate boundary equilibrium, the saddle-node and the Bogdanov-Takens bifurcations at the degenerate positive equilibrium and the Hopf bifurcation around the weak focus. The comparative study demonstrates that the dynamics are far richer and more complex than that of the system without cooperative hunting among predators. The analysis results reveal that appropriate intensity of cooperative hunting among predators is beneficial for the persistence of predators and the diversity of ecosystem.

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