PD Bifurcation and Chaos Behavior in a Predator-Prey Model With Allee Effect and Seasonal Perturbation

2019 ◽  
pp. 211-232
Author(s):  
Afef Ben Saad ◽  
Olfa Boubaker ◽  
Zeraoulia Elhadj
Keyword(s):  
Allee Effect ◽  
Bifurcation And Chaos ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

An Eco-Epidemic Predator–Prey Model with Allee Effect in Prey

2020 ◽  
Vol 30 (13) ◽  
pp. 2050194
Author(s):  
Absos Ali Shaikh ◽  
Harekrishna Das
Keyword(s):  
Allee Effect ◽  
Predator Population ◽  
Bifurcation And Chaos ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Disease In Predator ◽  
The Stability ◽  
The Impact ◽  
Existence Of Equilibria

This article describes the dynamics of a predator–prey model with disease in predator population and prey population subject to Allee effect. The positivity and boundedness of the solutions of the system have been determined. The existence of equilibria of the system and the stability of those equilibria are analyzed when Allee effect is present. The main objective of this study is to investigate the impact of Allee effect and it is observed that the system experiences Hopf bifurcation and chaos due to Allee effect. The results obtained from the model may be useful for analyzing the real-world ecological and eco-epidemiological systems.

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.

BIFURCATION AND CHAOS IN A DISCRETE PREDATOR–PREY MODEL WITH HOLLING TYPE-III FUNCTIONAL RESPONSE AND HARVESTING EFFECT

2021 ◽  
pp. 1-28
Author(s):  
ANURAJ SINGH ◽  
PREETI DEOLIA
Keyword(s):  
Functional Response ◽  
Sufficient Conditions ◽  
Flip Bifurcation ◽  
Bifurcation Structure ◽  
Bifurcation And Chaos ◽  
Predator Prey ◽  
Type Iii ◽  
Predator Prey Model ◽  
Prey Model ◽  
Wide Range

In this paper, we study a discrete-time predator–prey model with Holling type-III functional response and harvesting in both species. A detailed bifurcation analysis, depending on some parameter, reveals a rich bifurcation structure, including transcritical bifurcation, flip bifurcation and Neimark–Sacker bifurcation. However, some sufficient conditions to guarantee the global asymptotic stability of the trivial fixed point and unique positive fixed points are also given. The existence of chaos in the sense of Li–Yorke has been established for the discrete system. The extensive numerical simulations are given to support the analytical findings. The system exhibits flip bifurcation and Neimark–Sacker bifurcation followed by wide range of dense chaos. Further, the chaos occurred in the system can be controlled by choosing suitable value of prey harvesting.

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
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