Persistence and propagation of a discrete-time map and PDE hybrid model with strong Allee effect

2021 ◽  
Vol 61 ◽  
pp. 103336
Author(s):  
Zhenkun Wang ◽  
Yurij Salmaniw ◽  
Hao Wang
Keyword(s):  
Hybrid Model ◽  
Discrete Time ◽  
Allee Effect ◽  
Time Map ◽  
Strong Allee Effect

Interplay between strong Allee effect, harvesting and hydra effect of a single population discrete-time system

2015 ◽  
Vol 09 (01) ◽  
pp. 1650004 ◽  
Author(s):  
Debaldev Jana ◽  
Elsayed M. Elsayed
Keyword(s):  
Discrete Time ◽  
Allee Effect ◽  
Discrete Time System ◽  
Single Population ◽  
Dynamical Behaviors ◽  
System Generation ◽  
Stock Recruitment ◽  
Hydra Effect ◽  
Strong Allee Effect ◽  
Recruitment Model

The dynamics of a single population with non-overlapping generations can be described deterministically by a scalar difference equation in this study. A discrete-time Beverton–Holt stock recruitment model with Allee effect, harvesting and hydra effect is proposed and studied. Model with strong Allee effect results from incorporating mate limitation in the Beverton–Holt model. We show that these simple models exhibit some interesting (and sometimes unexpected) phenomena such as the hydra effect, sudden collapses and essential extinction. Along with this, harvesting is a socio-economic issue to continue any system generation after generation. Different dynamical behaviors for these situations have been illustrated numerically also. The biological implications of our analytical and numerical findings are discussed critically.

Dynamics and bifurcations of a discrete-time prey-predator model with Allee effect on the prey population

2021 ◽  
Vol 48 ◽  
pp. 100962
Author(s):  
Z. Eskandari ◽  
J. Alidousti ◽  
Z. Avazzadeh ◽  
J.A. Tenreiro Machado
Keyword(s):  
Discrete Time ◽  
Allee Effect ◽  
Prey Population ◽  
Predator Model

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.

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