Spatiotemporal Patterns in a Diffusive Predator-Prey Model with Prey Social Behavior

2019 ◽  
Vol 169 (1) ◽  
pp. 125-143 ◽  
Author(s):  
Salih Djilali ◽  
Soufiane Bentout
Keyword(s):  
Social Behavior ◽  
Spatiotemporal Patterns ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

Delayed predator–prey model with prey social behavior

2021 ◽  
Vol 136 (9) ◽  
Author(s):  
Salih Djilali ◽  
Carlo Cattani ◽  
Lakshmi Narayan Guin
Keyword(s):  
Social Behavior ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

Spatiotemporal patterns induced by cross-diffusion in predator–prey model with prey herd shape effect

2020 ◽  
Vol 13 (04) ◽  
pp. 2050030 ◽  
Author(s):  
Salih Djilali
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Point ◽  
Spatiotemporal Patterns ◽  
Shape Effect ◽  
Hopf Bifurcation Point ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Predator Prey Model ◽  
Prey Model ◽  
The Impact

In this paper, we investigate a predator–prey model with herd behavior and cross-diffusion subject to the zero flux boundary conditions. First, the temporal behavior of the model has been investigated, where Hopf bifurcation has been obtained. Then, by analyzing the characteristic equation it has been proved that the cross-diffusion generate a complex dynamics such as Hopf bifurcation, Turing instability, even Turing–Hopf bifurcation. Further, the impact of the prey herd shape on the spatiotemporal patterns has been discussed. Furthermore, by computing and analyzing the normal form associated with the Turing–Hopf bifurcation point, the spatiotemporal dynamics near the Turing–Hopf bifurcation point has been discussed and also justified by some numerical simulations.

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