scholarly journals Stability of patterns and of constant steady states for a cross-diffusion system

2016 ◽  
Vol 293 ◽  
pp. 208-216 ◽  
Author(s):  
G. Svantnerné Sebestyén ◽  
István Faragó ◽  
Róbert Horváth ◽  
R. Kersner ◽  
M. Klincsik
Keyword(s):  
Steady States ◽  
Diffusion System ◽  
Cross Diffusion

On a cross-diffusion system arising in image denoising

2018 ◽  
Vol 76 (5) ◽  
pp. 984-996 ◽  
Author(s):  
Gonzalo Galiano ◽  
Julián Velasco
Keyword(s):  
Image Denoising ◽  
Diffusion System ◽  
Cross Diffusion

Coexistence states in a cross-diffusion system of a predator–prey model with predator satiation term

2018 ◽  
Vol 28 (11) ◽  
pp. 2131-2159 ◽  
Author(s):  
Willian Cintra ◽  
Cristian Morales-Rodrigo ◽  
Antonio Suárez
Keyword(s):  
A Priori ◽  
Diffusion System ◽  
Predator Satiation ◽  
Linear Diffusion ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Predator Prey Model ◽  
Prey Model ◽  
Coexistence States ◽  
Predator Model

In this paper, we study the existence and non-existence of coexistence states for a cross-diffusion system arising from a prey–predator model with a predator satiation term. We use mainly bifurcation methods and a priori bounds to obtain our results. This leads us to study the coexistence region and compare our results with the classical linear diffusion predator–prey model. Our results suggest that when there is no abundance of prey, the predator needs to be a good hunter to survive.

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