Coexistence states for Lotka-Volterra systems with cross-diffusion

2000 ◽  
pp. 551-564
Author(s):  
Yoshio Yamada
Keyword(s):  
Cross Diffusion ◽  
Volterra Systems ◽  
Coexistence States

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.

Coexistence states of a predator–prey model with cross-diffusion

2018 ◽  
Vol 41 ◽  
pp. 179-203 ◽  
Author(s):  
Hailong Yuan ◽  
Jianhua Wu ◽  
Yunfeng Jia ◽  
Hua Nie
Keyword(s):  
Predator Prey ◽  
Cross Diffusion ◽  
Predator Prey Model ◽  
Prey Model ◽  
Coexistence States

scholarly journals Coexistence states of a Holling type II predator-prey system with self and cross-diffusion terms

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Willian Cintra ◽  
Carlos Alberto dos Santos ◽  
Jiazheng Zhou
Keyword(s):  
Global Bifurcation ◽  
Reaction Diffusion ◽  
Type Ii ◽  
Predator Prey ◽  
Self Diffusion ◽  
Cross Diffusion ◽  
Predator Prey Model ◽  
Coexistence States ◽  
Global Bifurcation Theory ◽  
Type Ii Functional Response

<p style='text-indent:20px;'>In this paper, we present results about existence and non-existence of coexistence states for a reaction-diffusion predator-prey model with the two species living in a bounded region with inhospitable boundary and Holling type II functional response. The predator is a specialist and presents self-diffusion and cross-diffusion behavior. We show the existence of coexistence states by combining global bifurcation theory with the method of sub- and supersolutions.</p>

Coexistence in a mutualistic model with cross-diffusion in a heterogeneous environment

2018 ◽  
Vol 11 (06) ◽  
pp. 1850078
Author(s):  
Badradeen Adam ◽  
Zhigui Lin ◽  
Abdelrazig K. Tarboush
Keyword(s):  
Environmental Heterogeneity ◽  
Eigenvalue Problems ◽  
Sufficient Conditions ◽  
Heterogeneous Environment ◽  
Free Diffusion ◽  
Cross Diffusion ◽  
Monotone Iterative ◽  
Mutualistic Interaction ◽  
Coexistence States ◽  
The Impact

To understand the impact of environmental heterogeneity and mutualistic interaction of species, we consider a mutualistic model with cross-diffusion in a heterogeneous environment. Semi-coexistence states have been studied by using the corresponding eigenvalue problems, and sufficient conditions for the existence and non-existence of coexistence states are given. Our results show that the model possesses at least one coexistence solution if the intrinsic populations growth rates are big or free-diffusion and cross-diffusion coefficients are weak. Otherwise, the model have no coexistence solution. The true solutions are obtained by utilizing the monotone iterative schemes. In order to illustrate our analytical results, some numerical simulations are given.

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