一类捕食系统的定态分歧与稳定性  

Bifurcation and Stability of Steady-State Solutions to a Prey-Predator System

作　　者：付一平[1] 陈霞[2] 

机构地区：[1]华南理工大学数学科学学院 [2]广州市第六中学

出　　处：《华南理工大学学报（自然科学版）》2007年第8期109-113,共5页Journal of South China University of Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10471047);广东省自然科学基金资助项目(04020077)

摘　　要：应用分歧和摄动理论讨论了带有交叉扩散项的三种群捕食链系统的正定态解的存在性和稳定性.先后以食饵的出生率、第一捕食者的死亡率和第二捕食者的死亡率作为分歧参数,利用线性化稳定性原理,逐步得到弱半平凡解、强半平凡解和非平凡解,并给出了关于这些分歧解的稳定性条件.Based on the bifurcation and perturbation theories, the existence and stability of the steady-state solutions to a prey-predator system of three species with cross-diffusion are discussed. Then, by taking the birth rate of the prey, the death rate of the first predator and the death rate of the second predator as the bifurcation parameters in order, the weak semi-trivial solution bifurcated from the trivial one, the strong semi-trivial solution bifurcated from the weak one and the nontrivial solution are all respectively obtained. The stability conditions for all the bifurcated solutions are finally presented in the paper.

关 键 词：交叉扩散系统 分歧 定态解 渐近稳定性 

分 类 号：O175.29[理学—数学]