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首页> 外文期刊>Advances in decision sciences >Global properties of the three-dimensionalpredator-prey Lotka-Volterra systems
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Global properties of the three-dimensionalpredator-prey Lotka-Volterra systems

机译：三维捕食者—食饵Lotka-Volterra系统的全局性质

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摘要

The global properties of the classical three-dimensional Lotka-Volterra two prey-onepredator and one prey-two predator systems, under the assumption that competition canbe neglected, are analysed with the direct Lyapunov method. It is shown that, except for apathological case, one species is always driven to extinction, and the system behaves asymptoticallyas a two-dimensional predator-prey Lotka-Volterra system. The same approach can be easilyextended to systems with many prey species and one predator, or many predator species and oneprey, and the same conclusion holds. The situation considered is common for New Zealand wild life,where indigenous and introduced species interact with devastating consequences for the indigenousspecies. According to our results the New Zealand indigenous species are definitely driven toextinction, not only in consequence of unsuccessful competition, but even when competition isabsent. This result leads to a better understanding of the mechanism of natural selection, andgives a new insight into pest control practice.
机译：在不考虑竞争的前提下，采用直接李雅普诺夫方法分析了经典三维Lotka-Volterra两食肉一捕食者系统和一食肉两捕食者系统的全局性质。结果表明，除无病理情况外，一个物种总是被驱赶灭绝，并且该系统表现为与二维捕食者—食饵Lotka-Volterra系统一样的渐近性。可以轻松地将相同的方法扩展到具有多个猎物种类和一个捕食者，或者具有许多捕食者种类和一个猎物的系统，并且得出相同的结论。所考虑的情况在新西兰的野生生物中很常见，在该物种中，土著和外来物种相互作用对土著物种造成毁灭性后果。根据我们的研究结果，新西兰本土物种的灭绝是肯定的，这不仅是由于竞争失败造成的，而且甚至是在竞争不存在的情况下。这一结果使人们对自然选择的机制有了更好的了解，并为害虫防治实践提供了新的见识。

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