scholarly journals Allee Effect in Gause Type Predator-Prey Models: Existence of Multiple Attractors, Limit cycles and Separatrix Curves. A Brief Review

2013 ◽  
Vol 8 (6) ◽  
pp. 143-164 ◽  
Author(s):  
E. González-Olivares ◽  
A. Rojas-Palma
Keyword(s):  
Limit Cycles ◽  
Allee Effect ◽  
Multiple Attractors ◽  
Predator Prey ◽  
Predator Prey Models

scholarly journals Predator–Prey Models: A Review of Some Recent Advances

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1783
Author(s):  
Érika Diz-Pita ◽  
M. Victoria Otero-Espinar
Keyword(s):  
Global Stability ◽  
Limit Cycles ◽  
Allee Effect ◽  
State Of The Art ◽  
Predator Prey ◽  
Local And Global Stability ◽  
Interacting Species ◽  
Fear Effect ◽  
Recent Advances ◽  
Predator Prey Models

In recent years, predator–prey systems have increased their applications and have given rise to systems which represent more accurately different biological issues that appear in the context of interacting species. Our aim in this paper is to give a state-of-the-art review of recent predator–prey models which include some interesting characteristics such as Allee effect, fear effect, cannibalism, and immigration. We compare the qualitative results obtained for each of them, particularly regarding the equilibria, local and global stability, and the existence of limit cycles.

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

Slow-fast limit cycles in predator-prey models

1992 ◽  
Vol 61 (3-4) ◽  
pp. 287-308 ◽  
Author(s):  
S. Rinaldi ◽  
S. Muratori
Keyword(s):  
Limit Cycles ◽  
Predator Prey ◽  
Predator Prey Models

scholarly journals Multiple limit cycles in a Leslie–Gower-type predator–prey model considering weak Allee effect on prey

2017 ◽  
Vol 22 (3) ◽  
pp. 347-365 ◽  
Author(s):  
Eduardo González-Olivares ◽  
◽  
Alejandro Rojas-Palma ◽  
Betsabé González-Yañez ◽  
◽  
...  
Keyword(s):  
Limit Cycles ◽  
Allee Effect ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

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.

Limit cycles in predator-prey models

1990 ◽  
Vol 98 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Dariusz M. Wrzosek
Keyword(s):  
Limit Cycles ◽  
Predator Prey ◽  
Predator Prey Models
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