具有凹非线性的合作种群动力学的尖锐季节阈值性质
Sharp seasonal threshold property for cooperative population dynamics with concave nonlinearities
摘要：
我们考虑一个生物种群，它的环境随时间周期性地变化，表现出两个非常不同的“季节”：一个是有利的，另一个是不利的。对于具有凹非线性项的单调微分模型，我们讨论了如下问题：在系统周期固定的情况下，在什么条件下存在不利季节的临界持续时间？所谓“临界持续时间”，我们的意思是，在某个阈值以上，人口不能维持和退出，而在这个阈值以下，系统收敛到一个唯一的周期和积极的解决方案。我们称之为“尖锐的季节阈值属性”（简称SSTP）。建立在以前的结果，我们得到的充分条件SSTP在任何维度和应用我们的标准，以一个二维模型，具有少年和成年种群的昆虫。
英文摘要：
We consider a biological population whose environment varies periodically in time, exhibiting two very different "seasons" : one is favorable and the other one is unfavorable. For monotone differential models with concave nonlinearities, we address the following question: the system's period being fixed, under what conditions does there exist a critical duration for the unfavorable season? By "critical duration" we mean that above some threshold, the population cannot sustain and extincts, while below this threshold, the system converges to a unique periodic and positive solution. We term this a "sharp seasonal threshold property" (SSTP, for short). Building upon a previous result, we obtain sufficient conditions for SSTP in any dimension and apply our criterion to a two-dimensional model featuring juvenile and adult populations of insects.
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