一类n维Nicholson系统的持久性、持久性和全局稳定性
Persistence, permanence and global stability for an n-dimensional Nicholson system
摘要：
对于一类具有多个离散时滞和斑块结构的Nicholson苍蝇系统，我们分析了其解的全局渐近性态的几个特征。结果表明，如果谱界的社区矩阵是非正的，那么人口成为灭绝的每一个补丁，而总人口一致持续，如果谱界是积极的。给出了解的渐近性态的一致上下界上界。当种群一致持续生存时，建立了唯一正平衡点的存在性，并给出了全局绝对渐近稳定性的严格判据，改进了最近文献中的结果.虽然我们的系统是不合作的，几个尖锐的阈值类型的结果，其动态证明，即使当社区矩阵是可约的，一种情况下，通常不会在文献中处理。
英文摘要：
For a Nicholson's blowflies system with patch structure and multiple discrete delays, we analyze several features of the global asymptotic behavior of its solutions. It is shown that if the spectral bound of the community matrix is non-positive, then the population becomes extinct on each patch, whereas the total population uniformly persists if the spectral bound is positive. Explicit uniform lower and upper bounds for the asymptotic behavior of solutions are also given. When the population uniformly persists, the existence of a unique positive equilibrium is established, as well as a sharp criterion for its absolute global asymptotic stability, improving results in the recent literature. While our system is not cooperative, several sharp threshold-type results about its dynamics are proven, even when the community matrix is reducible, a case usually not treated in the literature.
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