Dynamics of a predator-prey model with Allee effect and prey group defense

2015 ◽  
Author(s):  
Khairul Saleh
Keyword(s):  
Allee Effect ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Group ◽  
Prey Model ◽  
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.

scholarly journals The dynamics of a Leslie type predator–prey model with fear and Allee effect

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. Vinoth ◽  
R. Sivasamy ◽  
K. Sathiyanathan ◽  
Bundit Unyong ◽  
Grienggrai Rajchakit ◽  
...  
Keyword(s):  
Local Stability ◽  
Allee Effect ◽  
Jacobian Matrix ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fear Effect ◽  
Prey Model ◽  
Lyapunov Coefficient ◽  
Points Of View ◽  
Two Parameter

AbstractIn this article, we discuss the dynamics of a Leslie–Gower ratio-dependent predator–prey model incorporating fear in the prey population. Moreover, the Allee effect in the predator growth is added into account from both biological and mathematical points of view. We explore the influence of the Allee and fear effect on the existence of all positive equilibria. Furthermore, the local stability properties and possible bifurcation behaviors of the proposed system about positive equilibria are discussed with the help of trace and determinant values of the Jacobian matrix. With the help of Sotomayor’s theorem, the conditions for existence of saddle-node bifurcation are derived. Also, we show that the proposed system admits limit cycle dynamics, and its stability is discussed with the value of first Lyapunov coefficient. Moreover, the numerical simulations including phase portrait, one- and two-parameter bifurcation diagrams are performed to validate our important findings.

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

Stochastic predator–prey model with Allee effect on prey

2013 ◽  
Vol 14 (1) ◽  
pp. 768-779 ◽  
Author(s):  
Pablo Aguirre ◽  
Eduardo González-Olivares ◽  
Soledad Torres
Keyword(s):  
Allee Effect ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

Corrigendum to “Multiple stability and uniqueness of the limit cycle in a Gause-type predator–prey model considering the Allee effect on prey” [Nonlinear Anal. RWA 12 (2011) 2931–2942]

2013 ◽  
Vol 14 (1) ◽  
pp. 888-891
Author(s):  
Eduardo González-Olivares ◽  
Héctor Meneses-Alcay ◽  
Betsabé González-Yañez ◽  
Jaime Mena-Lorca ◽  
Alejandro Rojas-Palma ◽  
...  
Keyword(s):  
Limit Cycle ◽  
Allee Effect ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Nonlinear Anal ◽  
Prey Model ◽  
Multiple Stability

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.

Sign in / Sign up

Export Citation Format

Share Document