[1] Chen Bin, Xu Zhifen,. Note on a diffusive ratio-dependent predator-prey model [J]. Journal of Southeast University (English Edition), 2006, 22 (2): 294-296. [doi:10.3969/j.issn.1003-7985.2006.02.030]

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Note on a diffusive ratio-dependent predator-prey model()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

22

Issue:

2006 2

Page:

294-296

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2006-06-30

Info

Title:

Note on a diffusive ratio-dependent predator-prey model

Author(s):

Chen Bin¹;  2;  Xu Zhifen¹

¹Department of Mathematics, Southeast University, Nanjing 210096, China
²Department of Mathematics, Yancheng Teachers College, Yancheng 224002, China

Keywords:

ratio-dependent predator-prey model;  global stability;  comparison principle;  iteration

PACS:

O175.26

DOI:

10.3969/j.issn.1003-7985.2006.02.030

Abstract:

Subject to the homogeneous Neumann boundary condition, a ratio-dependent predator-prey reaction diffusion model is discussed.An improved result for the model is derived, that is, the unique positive constant steady state is the global stability.This is done using the comparison principle and establishing iteration schemes involving positive solutions supremum and infimum.The result indicates that the two species will ultimately distribute homogeneously in space.In fact, the comparison argument and iteration technique to be used in this paper can be applied to some other models.This method deals with the not-existence of a non-constant positive steady state for some reaction diffusion systems, which is rather simple but sufficiently effective.

References:

[1] Pang P Y H, Wang M X.Qualitative analysis of a ratio-dependent predator-prey system with diffusion [J].Proc Roy Soc Edinburgh, 2003, 133A(4):919-942.
[2] Kuang Y, Beretta E.Global qualitative analysis of a ratio-dependent predator-prey system[J].J Math Biol, 1998, 36(4):389-406.
[3] Hsu S B, Huang T W, Kuang Y.Global analysis of the Michaelis-Menten type ratio-dependent predator-prey system[J].J Math Biol, 2001, 42(6):489-506.
[4] Peng R, Wang M X.Note on a ratio-dependent predator-prey system with diffusion[J].Nonlinear Analysis, RWA, 2006, 7(1):1-11.
[5] Brown P N.Decay to uniform states in ecological interactions [J]. SIMA J Appl Math, 1980, 38(6):22-37.
[6] De Mottoni P, Rothe F.Convergence to homogeneous equilibrium state for generalized Volterra-Lotka system with diffusion [J].SIAM J Appl Math, 1979, 37(3):648-663.
[7] Aziz-Alaoui M A, Okiye M D.Boundedness and global stability for a predator-prey model with modified Leslie-Gower and Holling-Type Ⅱ Schemes [J].Appl Math Letter, 2003, 16(7):1069-1075.

Memo

Memo:

Biography: Chen Bin(1972—), male, graduate, lecturer, chenbin06@yahoo.com.cn.

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