Large speed traveling waves for the Rosenzweig–MacArthur predator–prey model with spatial diffusion

2021 ◽  
Vol 415 ◽  
pp. 132730
Author(s):  
Arnaud Ducrot ◽  
Zhihua Liu ◽  
Pierre Magal
Keyword(s):  
Traveling Waves ◽  
Spatial Diffusion ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Large Speed

scholarly journals Traveling waves for a generalized Holling–Tanner predator–prey model

2017 ◽  
Vol 263 (11) ◽  
pp. 7782-7814 ◽  
Author(s):  
Shangbing Ai ◽  
Yihong Du ◽  
Rui Peng
Keyword(s):  
Traveling Waves ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals Mathematical analysis of a diffusive predator-prey model with herd behavior and prey escaping

2020 ◽  
Vol 15 ◽  
pp. 23 ◽  
Author(s):  
Fethi Souna ◽  
Salih Djilali ◽  
Fayssal Charif
Keyword(s):  
Hopf Bifurcation ◽  
Center Manifold ◽  
State Density ◽  
Spatial Diffusion ◽  
Herd Behavior ◽  
New Approach ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Diffusive System

In this paper, we consider a new approach of prey escaping from herd in a predator-prey model with the presence of spatial diffusion. First, the sensitivity of the equilibrium state density with respect to the escaping rate has been studied. Then, the analysis of the non diffusive system was investigated where boundedness, local, global stability, Hopf bifurcation are obtained. Besides, for the diffusive system, we proved the occurrence of Hopf bifurcation and the non existence of diffusion driven instability. Furthermore, the direction of Hopf bifurcation has been proved using the normal form on the center manifold. Some numerical simulations have been used to illustrate the obtained results.

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