Spatiotemporal dynamics in a diffusive predator–prey model with group defense and nonlocal competition

2020 ◽  
Vol 103 ◽  
pp. 106175 ◽  
Author(s):  
Yaqi Liu ◽  
Daifeng Duan ◽  
Ben Niu
Keyword(s):  
Spatiotemporal Dynamics ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Group Defense

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 Spatiotemporal dynamics of a diffusive predator-prey model with generalist predator

2020 ◽  
Vol 13 (11) ◽  
pp. 2949-2973
Author(s):  
Dingyong Bai ◽  
◽  
Jianshe Yu ◽  
Yun Kang ◽  
◽  
...  
Keyword(s):  
Spatiotemporal Dynamics ◽  
Generalist Predator ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model
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