一类异质环境下HollingⅡ型竞争模型的稳态解

Steady-state solutions of a Holling typeⅡcompetition model in heterogeneous environment

研究一类异质环境下具有HollingⅡ型功能反应函数的竞争模型的稳态解。利用线性算子的谱理论和抛物方程的比较原理得到模型平凡解和半平凡解的全局渐近稳定性,得出该竞争模型中两物种竞争排斥的充分条件。进一步,借助拓扑度理论,得到正稳态解存在的充分条件,从而给出该竞争模型中两物种共存的充分条件。

The steady-state solutions of a competitive model with Holling typeⅡfunctional response function in heterogeneous environment is investigated.Using the spectral theory of linear operators and comparison principle of parabolic equations,the global asymptotic stability of the trivial and semi-trivial solutions of the model is obtained,and the sufficient conditions for the competitive repulsion of two species are derived.With the help of topological degree theory,the sufficient conditions for the existence of positive steady-state solutions are established,which gives the sufficient conditions for the coexistence of the two species.