三种群捕食系统的正定常稳定解

应用分歧和摄动理论讨论了带有反应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．由于三种群系统的复杂性，讨论过程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正解，并证明了这些分歧解为渐近稳定的．所得结论与原系统模型的生态学意义相符．

The Existence and Stability of Positive Steady-State Communal Solutions for a Predator-Prey System of Three Species

By using the bifurcation theory and perturbation theory of the simple eigenvalue, the existence and stability of the positive steady-state communal solutions for a predator-prey system of three species are discussed. Let the birth rate of the prey be taken as a bifurcation parameter, the weak semi-trivial solution (u, 0, 0) bifurcated from the trivial one is obtained- Then the strong semi-trivial solution (u,v, 0) bifurcated from the weak one (u, 0, 0) is obtained by taking the death rate of the first predator as a bifurcation parameter also. Finally, the positive nontrivial solution (u *,v*,w* ) bifurcated from (u,v,0) is obtained by again taking the death rate of the second predator as a bifurcation parameter. All the solutions obtained are proved to be asymptotically stable.