Global stability and stationary pattern of a diffusive prey-predator model with modified Leslie-Gower term and Holling II functional response
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Authors
Yan Li
- College of Science, China University of Petroleum (East China), Qingdao 266580, P. R. China.
Xinhong Zhang
- College of Science, China University of Petroleum (East China), Qingdao 266580, P. R. China.
Bingchen Liu
- College of Science, China University of Petroleum (East China), Qingdao 266580, P. R. China.
Abstract
This paper is concerned with a diffusive prey-predator model with modified Leslie-Gower term and
Holling II functional response subject to the homogeneous Neumann boundary condition. Firstly, by upper
and lower solutions method, we prove the global asymptotic stability of the unique positive constant
steady state solution. Secondly, introducing the cross diffusion, we obtain the existence of non-constant
positive solutions. The results demonstrate that under certain conditions, even though the unique positive
constant steady state is globally asymptotically stable for the model with self-diffusion, the non-constant
positive steady states can exist due to the emergency of cross-diffusion, that is to say, cross-diffusion can
create stationary pattern. Finally, using the bifurcation theory and treating cross diffusion as a bifurcation
parameter, we obtain the existence of positive non-constant solutions.
Share and Cite
ISRP Style
Yan Li, Xinhong Zhang, Bingchen Liu, Global stability and stationary pattern of a diffusive prey-predator model with modified Leslie-Gower term and Holling II functional response, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 5, 2527--2540
AMA Style
Li Yan, Zhang Xinhong, Liu Bingchen, Global stability and stationary pattern of a diffusive prey-predator model with modified Leslie-Gower term and Holling II functional response. J. Nonlinear Sci. Appl. (2016); 9(5):2527--2540
Chicago/Turabian Style
Li, Yan, Zhang, Xinhong, Liu, Bingchen. "Global stability and stationary pattern of a diffusive prey-predator model with modified Leslie-Gower term and Holling II functional response." Journal of Nonlinear Sciences and Applications, 9, no. 5 (2016): 2527--2540
Keywords
- Prey-predator model
- Leslie-Gower term
- upper and lower solutions method
- stationary pattern
- bifurcation.
MSC
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