一类捕食者-食饵模型中扩散的作用被引量：1

Effects of Diffusions in a Leslie-Gower Predator-prey Model

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摘要本文讨论捕食者带有交错扩散的修正的Leslie-Gower捕食者-食饵模型中各扩散系数的作用.得到的结果表明,交错扩散会导致模型唯一的正常数平衡点失稳.而食饵物种的自扩散则具有抑制失稳发生的作用. In this paper, the effects of diffusions in a modified Leslie-Gower predator-prey model with cross-diffusion are studied. It is shown that cross-diffusion can induce instability of the unique positive equilibrium in this model. While, the diffusion of prey species has a role on inhibiting instability.

作者张丽娜张晓杰

机构地区西北师范大学数学与统计学院

出处《应用数学》 CSCD 北大核心 2016年第3期672-677,共6页 Mathematica Applicata

基金国家自然科学基金(11061031)

关键词 Leslie-Gower捕食者-食饵模型交错扩散稳定性 Leslie-Gower predator-prey model Cross-diffusion Stability

分类号 O175.26 [理学—基础数学]

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参考文献5

1张丽娜,吴守妍.修正的Leslie-Gower捕食者-食饵扩散模型解的整体性态[J].山东大学学报（理学版）,2014,49(1):86-91. 被引量：2
2张丽娜,李月霞.修正的Leslie-Gower捕食者-食饵扩散模型正平衡点的全局渐近稳定[J].应用数学,2014,27(2):381-386. 被引量：3
3Shigesada N, Kawasaki K, Teramoto E. Spatial segregation of interacting species[J]. J. Theoret. Biol., 1979, 79:83-99.
4Duber B, Hussain B. A predator-prey interaction model with self- and cross-diffusion[J]. Ecological Modelling, 2001, 141(1):67-76.
5Kuto K, Yamada Y. Multiple coexistence states for a prey-predator system with cross-diffusion[J]. J. Differential Equations, 2004, 197:315-348.

二级参考文献13

1Leslie P H,Gower J C. The properties of a stochastic model for the predator-prey type of interaction be- tween two species[-j 7. Biometrica, 1960,47 : 219-234.
2Braza P A. The bifurcation structure of the Holling-Tanner model for predator-prey interactions using two-timing[-J ]. SIAM j. Appl. Math. , 2003,63 - 889-904.
3Hsu S B, Hwang T W. Global stability for a class of predator-prey systemsEJ]. SIAM J. Appl. Math. , 1995,55-763-783.
4Aziz-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. Lett. ,2003,16 - 1069-1075,.
5叶其孝.李正元,王明新,吴雅萍.反应扩散方程引论[M].第二版.北京:科学出版社.2011.
6DU Y H,HSU S B. A diffusive predator-prey model in heterogeneous environment[J].{H}Journal of Differential Equations,2004.331-364.
7DU Y H,WANG M X. Asymptotic behaviour of positive steady states to a predator-prey model[J].Proc Royal Soc Edin-burgh A,2006,(04):759-778.
8DU Y H,PENG R,WANG M X. Effect of a protection zone in the diffusive Leslie predator-prey model[J].J Differential E-quations,2009.3932-3956.
9PENG R,WANG M X. Positive steady-states of the Holling-Tanner prey-predator model with diffusion[J].Proc Roy Soc Ed-inburgh Sect A,2005.149-164.
10PENG R,WANG M X. Global stability of the equilibrium of a diffusive Holling-Tanner prey-predator model[J].{H}Appl Math Letters,2007.664-670.