Lotka-Volterra自治竞争系统的共存与绝灭(英文)

Coexistence and Extinction in Autonomous Competitive Lotka-Volterra Systems

研究了一类自治n种群Lotka-Volterra竞争系统.建立了一部分种群绝灭,另一部分种群持续生存新的判别准则,推广了已知相关结果.

In this paper, an automous n-species competitive Lotka-Volterra sys-tems are studied. For each r ≤n , we show that if the coefficients satisfy certaininequalities, then any solution with strictly positive initial values has the propertythat n - r of its components vanish, whilst the remaining r components asymptot-ically approach a canonical solution of an r-dimensional restricted system. In otherwords, r of the species being modeled survive whilst the remaining n - r are driven toextinction. Our results bridge the gap among all known relational results.