Permanence of discrete-time Kolmogorov systems for two species and saturated fixed points
Permanence of discrete-time Kolmogorov systems for two species and saturated fixed points
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DOI：
10.1007/s00285-003-0224-8
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发表时间：
2004
影响因子：
1.9
通讯作者：
R. Kon
中科院分区：
文献类型：
--
作者：
R. Kon
本文考虑两种群离散时间Kolmogorov系统的动力学问题。特别地，考虑了系统的持久性。持久性是描述物种共存的概念之一。利用平均Liapunov函数的方法，我们得到了系统持久生存的一个简单的充分条件。也就是说，在人口增长率函数具有适当的凸性或凹性的条件下，不存在饱和边界不动点就足以保证系统的持久性。数值研究表明，对于不具有这种性质的种群增长率函数系统，饱和边界不动点的不存在并不足以保证系统的持久性，实际上，尽管存在稳定共存不动点，边界周期轨道或混沌轨道仍能吸引人。这一结果特别暗示了稳定共存不动点的存在不足以保证系统的持久性。
This paper considers the dynamics of a discrete-time Kolmogorov system for two-species populations. In particular, permanence of the system is considered. Permanence is one of the concepts to describe the species’ coexistence. By using the method of an average Liapunov function, we have found a simple sufficient condition for permanence of the system. That is, nonexistence of saturated boundary fixed points is enough for permanence of the system under some appropriate convexity or concavity properties for the population growth rate functions. Numerical investigations show that for the system with population growth rate functions without such properties, the nonexistence of saturated boundary fixed points is not sufficient for permanence, actually a boundary periodic orbit or a chaotic orbit can be attractive despite the existence of a stable coexistence fixed point. This result implies, in particular, that existence of a stable coexistence fixed point is not sufficient for permanence.