一类带饱和项互惠模型平衡态解的稳定性

Stability States for Cooperative Model with Saturation

文章研究了一类两个物种同时带饱和项的互惠模型在第一边界值条件下的平衡态解的稳定性.首先给出了此类模型的平衡态方程解的情况,然后运用线性算子的特征值理论讨论了其平凡解、半平凡解的稳定性,最后运用扰动理论和分歧解的稳定性理论分别得到了λ1-c<a<λ1和a<λ1在两种情况下正解分支的稳定性情况.

The stability on a kind of solutions of the steady-state system, with respect to a class of cooperative system with saturating interaction terms for two species under the first boundary conditions,is discussed. First, the solutions of the steady-state system are given. Then, the stability of the trivial solution and the semi-trivial solution is established by the eigenvalue theorem for linear operators. Finally, the stability of the positive solutions at two semi-trivial solutions for two classes （λ1-c〈a〈λ1and α〈λ1））is obtained respectively by perturbation theorem and the stability theorem for bifurcation solution.