Codimension-one and codimension-two bifurcations of a discrete predator–prey system with strong Allee effect

2019 ◽  
Vol 162 ◽  
pp. 155-178 ◽  
Author(s):  
Limin Zhang ◽  
Chaofeng Zhang ◽  
Zhirong He
Keyword(s):  
Allee Effect ◽  
Predator Prey ◽  
Codimension Two ◽  
Codimension One ◽  
Prey System ◽  
Strong Allee Effect

Bogdanov–Takens bifurcation with codimension three of a predator–prey system suffering the additive Allee effect

2017 ◽  
Vol 10 (03) ◽  
pp. 1750044 ◽  
Author(s):  
Yanwei Liu ◽  
Zengrong Liu ◽  
Ruiqi Wang
Keyword(s):  
Allee Effect ◽  
Perturbation Parameter ◽  
Parameter Plane ◽  
Predator Prey ◽  
Numerical Examples ◽  
Codimension Two ◽  
Prey System ◽  
Existence Conditions ◽  
Parameter Dependent

In the present work, research efforts have focused on investigating codimension two and three Bogdanov–Takens bifurcations of a predator–prey system with additive Allee effect. According to the existence conditions of Bogdanov–Takens bifurcation, we give the associated generic unfolding, and derive the dynamical classification in the perturbation parameter plane using some smooth parameter-dependent transformations of coordinate. Moreover, some numerical examples and simulations are performed to complete and illustrate our results.

Predator–prey system with strong Allee effect in prey

2010 ◽  
Vol 62 (3) ◽  
pp. 291-331 ◽  
Author(s):  
Jinfeng Wang ◽  
Junping Shi ◽  
Junjie Wei
Keyword(s):  
Allee Effect ◽  
Predator Prey ◽  
Prey System ◽  
Strong Allee Effect

scholarly journals Dynamics in a diffusive predator-prey system with stage structure and strong allee effect

2020 ◽  
Vol 19 (2) ◽  
pp. 883-910
Author(s):  
Yuying Liu ◽  
◽  
Yuxiao Guo ◽  
Junjie Wei ◽  
◽  
...  
Keyword(s):  
Allee Effect ◽  
Stage Structure ◽  
Predator Prey ◽  
Prey System ◽  
Strong Allee Effect

The Effects of Stochasticity on Pattern Formation in a Space- and Time-Discrete Predator–Prey System with Strong Allee Effect in the Prey

2019 ◽  
Vol 81 (5) ◽  
pp. 1369-1393
Author(s):  
Joice Chaves Marques ◽  
Horst Malchow ◽  
Luiz Alberto Díaz Rodrigues ◽  
Diomar Cristina Mistro
Keyword(s):  
Pattern Formation ◽  
Allee Effect ◽  
Predator Prey ◽  
Space And Time ◽  
Prey System ◽  
Strong Allee Effect

scholarly journals Double Hopf bifurcation of a diffusive predator–prey system with strong Allee effect and two delays

2021 ◽  
Vol 26 (1) ◽  
pp. 72-92
Author(s):  
Yuying Liu ◽  
Junjie Wei
Keyword(s):  
Hopf Bifurcation ◽  
Allee Effect ◽  
Bifurcation Theorem ◽  
Predator Prey ◽  
Double Hopf Bifurcation ◽  
Prey System ◽  
Two Delays ◽  
Strong Allee Effect ◽  
The Stability ◽  
Two Parameters

In this paper, we consider a diffusive predator–prey system with strong Allee effect and two delays. First, we explore the stability region of the positive constant steady state by calculating the stability switching curves. Then we derive the Hopf and double Hopf bifurcation theorem via the crossing directions of the stability switching curves. Moreover, we calculate the normal forms near the double Hopf singularities by taking two delays as parameters. We carry out some numerical simulations for illustrating the theoretical results. Both theoretical analysis and numerical simulation show that the system near double Hopf singularity has rich dynamics, including stable spatially homogeneous and inhomogeneous periodic solutions. Finally, we evaluate the influence of two parameters on the existence of double Hopf bifurcation.

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