一类互惠模型平衡解的分歧与稳定

Bifurcation and Stability of the Steady-state Solutions for a Cooperative Model

研究了一类具有饱和项的Volterra-Lotka互惠模型在齐次Neumann边界条件下正平衡的分歧与稳定。利用特征值分歧理论和谱分析方法,以b,a为分歧参数分别研究了当m=1和n=1时系统在常数平衡解(a～(1/α),0)和(0,b～(1/β))附近出现分歧现象,进而得到了该模型正平衡解存在的充分条件;同时运用线性算子的扰动理论和分歧解的稳定理论给出了分歧解的稳定性。

The bifurcation and the stability of the positive steady-state solutions of the Volterra- Lotka cooperative model with homogeneous Neumann boundary are investigated by the methods of spectral analysis and bifurcation the-ory . The bifurcations at the steady-state solution （a 1/α,0） and （0,b 1/β） for two cases m =1 and n = 1 are acquired by treating b and a as a bifurcation parameters. Some sufficient conditions for the existence of positive steady-state solution are given. Moreover, some stability results of the bifurcation solutions are obtained by using perturbation theory of linear operators and stability theory of bifurcation solutions.