Global properties of the three-dimensionalpredator-prey Lotka-Volterra systems

[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.

[学科分类] 自然科学（综合）