Multiple limit cycles in predator-prey models

1981 ◽  
Vol 11 (1) ◽  
pp. 51-63 ◽  
Author(s):  
Alan Hastings
Keyword(s):  
Limit Cycles ◽  
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

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

scholarly journals Multiple limit cycles for predator-prey models

1990 ◽  
Vol 99 (1) ◽  
pp. 71-75 ◽  
Author(s):  
Josef Hofbauer ◽  
Joseph W.-H. So
Keyword(s):  
Limit Cycles ◽  
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.

scholarly journals Limit Cycles in Predator-Prey Models

2017 ◽  
Vol 4 (1) ◽  
pp. 70-81
Author(s):  
Liliana Puchuri
Keyword(s):  
Limit Cycles ◽  
Predator Prey ◽  
Predator Prey Models

The global dynamics of stochastic Holling type II predator-prey models with non constant mortality rate

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5811-5825
Author(s):  
Xinhong Zhang
Keyword(s):  
Mortality Rate ◽  
Stochastic Model ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Global Dynamics ◽  
Type Ii ◽  
Predator Prey ◽  
Persistence In The Mean ◽  
The Mean ◽  
Predator Prey Models

In this paper we study the global dynamics of stochastic predator-prey models with non constant mortality rate and Holling type II response. Concretely, we establish sufficient conditions for the extinction and persistence in the mean of autonomous stochastic model and obtain a critical value between them. Then by constructing appropriate Lyapunov functions, we prove that there is a nontrivial positive periodic solution to the non-autonomous stochastic model. Finally, numerical examples are introduced to illustrate the results developed.

Plugging Space into Predator-Prey Models: An Empirical Approach

2006 ◽  
Vol 167 (2) ◽  
pp. 246
Author(s):  
Bergström ◽  
Englund ◽  
Leonardsson
Keyword(s):  
Empirical Approach ◽  
Predator Prey ◽  
Predator Prey Models
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