Dynamics of predator–prey models with a strong Allee effect on the prey and predator-dependent trophic functions

2016 ◽  
Vol 30 ◽  
pp. 143-169 ◽  
Author(s):  
G. Buffoni ◽  
M. Groppi ◽  
C. Soresina
Keyword(s):  
Allee Effect ◽  
Predator Prey ◽  
Strong Allee Effect ◽  
Predator Prey Models

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.

scholarly journals Stability and Bifurcation in a Predator–Prey Model with the Additive Allee Effect and the Fear Effect

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1280
Author(s):  
Liyun Lai ◽  
Zhenliang Zhu ◽  
Fengde Chen
Keyword(s):  
Allee Effect ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Predator Species ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fear Effect ◽  
Prey Model ◽  
Strong Allee Effect ◽  
Theoretical Results

We proposed and analyzed a predator–prey model with both the additive Allee effect and the fear effect in the prey. Firstly, we studied the existence and local stability of equilibria. Some sufficient conditions on the global stability of the positive equilibrium were established by applying the Dulac theorem. Those results indicate that some bifurcations occur. We then confirmed the occurrence of saddle-node bifurcation, transcritical bifurcation, and Hopf bifurcation. Those theoretical results were demonstrated with numerical simulations. In the bifurcation analysis, we only considered the effect of the strong Allee effect. Finally, we found that the stronger the fear effect, the smaller the density of predator species. However, the fear effect has no influence on the final density of the prey.

ALLEE EFFECT, EMIGRATION AND IMMIGRATION IN A CLASS OF PREDATOR-PREY MODELS

BIOMAT 2007 ◽  
2008 ◽  
Author(s):  
EDUARDO GONZÁLEZ-OLIVARES ◽  
JAIME MENA-LORCA ◽  
HÉCTOR MENESES-ALCAY ◽  
BETSABÉ GONZÁLEZ-YAÑEZ ◽  
JOSÉ D. FLORES
Keyword(s):  
Allee Effect ◽  
Emigration And Immigration ◽  
Predator Prey ◽  
Predator Prey Models

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 Phase tipping: how cyclic ecosystems respond to contemporary climate

2021 ◽  
Vol 477 (2254) ◽  
Author(s):  
Hassan Alkhayuon ◽  
Rebecca C. Tyson ◽  
Sebastian Wieczorek
Keyword(s):  
Allee Effect ◽  
Critical Factor ◽  
Global Dynamics ◽  
Tipping Points ◽  
Time Varying ◽  
Predator Prey ◽  
Critical Transitions ◽  
External Conditions ◽  
Predator Prey Models ◽  
Contemporary Climate

We identify the phase of a cycle as a new critical factor for tipping points (critical transitions) in cyclic systems subject to time-varying external conditions. As an example, we consider how contemporary climate variability induces tipping from a predator–prey cycle to extinction in two paradigmatic predator–prey models with an Allee effect. Our analysis of these examples uncovers a counterintuitive behaviour, which we call phase tipping or P-tipping , where tipping to extinction occurs only from certain phases of the cycle. To explain this behaviour, we combine global dynamics with set theory and introduce the concept of partial basin instability for attracting limit cycles. This concept provides a general framework to analyse and identify easily testable criteria for the occurrence of phase tipping in externally forced systems, and can be extended to more complicated attractors.

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