Predator-Prey Model with Prey Group Defense and Non-linear Predator Harvesting

2020 ◽  
pp. 109-125
Author(s):  
Rajat Kaushik ◽  
Sandip Banerjee
Keyword(s):  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Group ◽  
Prey Model ◽  
Non Linear ◽  
Group Defense

Bifurcation Analysis of a Delay-Induced Predator–Prey Model with Allee Effect and Prey Group Defense

2021 ◽  
Vol 31 (10) ◽  
pp. 2150158
Author(s):  
Yong Ye ◽  
Yi Zhao
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Allee Effect ◽  
Periodic Oscillation ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Group ◽  
Prey Model ◽  
Group Defense ◽  
The Stability

In this paper, we establish a predator–prey model with focus on the Allee effect and prey group defense. The positivity and boundedness of the model, existence of equilibrium point, and stability change caused by Allee effect are studied. Bifurcation (transcritical bifurcation, Hopf bifurcation) analysis is discussed, and the direction of Hopf bifurcation is determined by calculating the first Lyapunov number. Then we introduce delay into the original model and consider the influence of delay on the stability of the model. By selecting delay as the bifurcation parameter, we obtain the existence conditions of Hopf bifurcation and the direction of Hopf bifurcation. Finally, we verify the theoretical analysis by numerical simulation. Considering both the Allee effect and the prey group defense, the dynamic behavior near the origin becomes more complex than only considering Allee effect or prey group defense in the model. Allee effect can bring the risk of extinction and the change of stability, and the delay effect can make the stable coexistence equilibrium unstable and lead to periodic oscillation.

Dynamics of a stage-structured predator-prey model: cost and benefit of fear-induced group defense

2021 ◽  
pp. 110846
Author(s):  
Pijush Panday ◽  
Nikhil Pal ◽  
Sudip Samanta ◽  
Piotr Tryjanowski ◽  
Joydev Chattopadhyay
Keyword(s):  
Predator Prey ◽  
Cost And Benefit ◽  
Predator Prey Model ◽  
Prey Model ◽  
Group Defense

scholarly journals A predator-prey model with cooperative hunting in the predator and group defense in the prey

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yanfei Du ◽  
Ben Niu ◽  
Junjie Wei
Keyword(s):  
Hopf Bifurcation ◽  
Heteroclinic Orbits ◽  
Initial Population ◽  
Continuous Transition ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Cooperative Hunting ◽  
Prey Model ◽  
Existence And Stability ◽  
Group Defense

<p style='text-indent:20px;'>In this paper we propose a predator-prey model with a non-differentiable functional response in which the prey exhibits group defense and the predator exhibits cooperative hunting. There is a separatrix curve dividing the phase portrait. The species with initial population above the separatrix result in extinction of prey in finite time, and the species with initial population below it can coexist, oscillate sustainably or leave the prey surviving only. Detailed bifurcation analysis is carried out to explore the effect of cooperative hunting in the predator and aggregation in the prey on the existence and stability of the coexistence state as well as the dynamics of system. The model undergoes transcritical bifurcation, Hopf bifurcation, homoclinic (heteroclinic) bifurcation, saddle-node bifurcation, and Bogdanov-Takens bifurcation, and through numerical simulations it is found that it possesses rich dynamics including bubble loop of limit cycles, and open ended branch of periodic orbits disappearing through a homoclinic cycle or a loop of heteroclinic orbits. Also, a continuous transition of different types of Hopf branches are investigated which forms a global picture of Hopf bifurcation in the model.</p>

scholarly journals Taxis-driven pattern formation in a predator-prey model with group defense

2020 ◽  
Vol 43 ◽  
pp. 100848
Author(s):  
Merlin C. Köhnke ◽  
Ivo Siekmann ◽  
Horst Malchow
Keyword(s):  
Pattern Formation ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Group Defense
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