This paper is concerned about the S–K–T competition model with spatially heterogeneous interactions, in which the two competing species are identical in all aspects except for their interspecific competitions. Under small variations of interspecific competitions, a good understanding of the dynamics and the structure of the set of steady states is gained by the Lyapunov–Schmidt procedure and detailed analysis. The results reveal that the role that the spatial heterogeneity plays in the coexistence of the competing species can be rather interesting and complicated. Either stable or unstable coexistence state can be produced by suitable spatial heterogeneity, so the spatial heterogeneity can be either favorable or unfavorable for the coexistence of competing species.

本文关注的是具有空间异质相互作用的S–K–T竞争模型，其中两个竞争物种除了种间竞争外，所有方面都是相同的。在种间竞争的微小变化下，通过Lyapunov–Schmidt程序和详细分析，可以很好地了解动力学和稳态集的结构。结果表明，空间异质性在竞争物种共存中扮演的角色可能非常有趣且复杂。稳定的或不稳定的共存状态可以通过适当的空间异质性产生，因此空间异质性对于竞争物种的共存可能是有利的，也可能是不利的。