一类竞争扩散系统的全局动力学及其在修正Leslie-Gower模型中的应用
Global dynamics of a competition-diffusion system and application to a modified Leslie-Gower model
摘要：
研究了空间非均匀环境中一类特殊的Lotka-Volterra竞争扩散系统的全局动力学.该模型表明捕食者密度的演化与食饵密度无关。基于主谱理论和经典单种群Logistic模型的动力学，我们得到了该竞争扩散系统的全局动力学。作为应用，在适当的条件下，我们证明了一类非均匀环境中带扩散的修正Leslie-Gower模型平衡态的全局稳定性和两种群的持续生存性.
英文摘要：
We investigate the global dynamics of a special case of the classical Lotka-Volterra competition-diffusion system in spatially heterogeneous environment. This model indicates that the evolution of the density of the predator is independent of the density of the prey. Based on the principal spectral theory and the dynamics of the classical single-species logistic model, we obtain the global dynamics of this competition-diffusion system. As an application, under some suitable conditions we use the obtained results to prove the global stability of steady states and the persistence of the two species in a modified Leslie-Gower model with diffusion in heterogeneous environment.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
