We analyze the Lotka–Volterra n prey-1 predator system without any interspecific interaction between preys, in which each prey species has the relationship of apparent competition with any other prey species. The system we considered in this paper necessarily has a globally asymptotically stable unique equilibrium state. We find the necessary and sufficient condition to determine which equilibrium states becomes asymptotically stable. Then we consider the effect of the deletion of a native prey species and that of the invasion of an alien prey species on the stability of the system. We prove that the deletion of a prey species could not cause the secondary extinction of any other prey species but could make the predator go extinct. In contrast, if an alien prey species is successfully introduced into the system at the coexistent equilibrium state, the extinction of some native prey species could occur by the apparent competition effect. Moreover, such a successful introdu...

中文翻译：

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在Lotka–Volterra系统中，一个共享的捕食者可以与多少个猎物共存？：通过物种删除/引入进行状态转移

我们分析了Lotka–Volterra n猎物-1捕食者系统之间的猎物之间没有任何种间相互作用，其中每个猎物物种与任何其他猎物物种都有明显的竞争关系。我们在本文中考虑的系统必然具有全局渐近稳定的唯一平衡状态。我们找到了确定哪些平衡态渐近稳定的必要和充分条件。然后，我们考虑了删除本地猎物物种和入侵外来猎物物种对系统稳定性的影响。我们证明，猎物物种的删除不会导致任何其他猎物物种的继发性灭绝，但可以使捕食者灭绝。相反，如果将一个外来猎物物种成功地以共存的平衡状态引入系统，明显的竞争效应可能导致某些本地猎物物种的灭绝。而且，如此成功的介绍...