一类具扩散的环境数学模型的稳定性

Stability of an Environment Mathematical Model with Diffusion

许多环境数学模型是用常微分方程表示的,它只考虑了时间对种群密度的影响.研究了一类具扩散的环境数学模型,用反应扩散方程组来表示这些模型更显合理.首先利用比较原理讨论了抛物问题解的正性及有界性,然后运用上下解方法及相应的单调迭代序列研究其动力学行为,得到了正平衡点渐近稳定的充分条件.

Many environment mathematical models are ordinary differential equations where time is considered only as its effect on population density. An environment mathematical model with diffusion is discussed in this paper. It is reasonable for us to make use of reaction--diffusion e- quations to describe these models. The positivity and boundedness of the solution to the parabolic problem are first given by comparison, and the dynamics of the system is investigated using upper and lower solutions and the associated monotone iterations. Moreover, the sufficient conditions are obtained for the asymptotic stability of the positive equilibrium of the model.