scholarly journals Spatio-temporal oscillation for a singular predator–prey model

2018 ◽  
Vol 459 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Jong-Shenq Guo ◽  
Masahiko Shimojo
Keyword(s):  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Temporal Oscillation ◽  
Spatio Temporal

Spatio-Temporal Patterns of Predator–Prey Model with Allee Effect and Constant Stocking Rate for Predator

2021 ◽  
Vol 31 (16) ◽  
Author(s):  
Xuan Tian ◽  
Shangjiang Guo
Keyword(s):  
Steady State ◽  
Allee Effect ◽  
Sufficient Conditions ◽  
Steady State Solution ◽  
Turing Pattern ◽  
Stocking Rate ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Spatio Temporal

A diffusive predator–prey model with Allee effect and constant stocking rate for predator is investigated and it is shown that Allee effect is the decisive factor driving the formation of Turing pattern. Furthermore, it is observed that Turing pattern appears only when the diffusion rate of the prey is faster than that of the predator, which is just opposite to the condition of Turing pattern in the classical predator–prey system. Some sufficient conditions are obtained to ensure the asymptotical stability of a spatially homogeneous steady-state solution. The existence and nonexistence of positive nonconstant steady-state solutions are investigated to understand the mechanisms of generating spatiotemporal patterns. Furthermore, Hopf and steady-state bifurcations are analyzed in detail by using Lyapunov–Schmidt reduction.

scholarly journals Numerical solution of a spatio-temporal predator-prey model with infected prey

2019 ◽  
Vol 16 (1) ◽  
pp. 438-473 ◽  
Author(s):  
Raimund Bürger ◽  
◽  
Gerardo Chowell ◽  
Elvis Gavilán ◽  
Pep Mulet ◽  
...  
Keyword(s):  
Numerical Solution ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Spatio Temporal ◽  
Infected Prey
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