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arXiv · 1804.07641

Sharp seasonal threshold property for cooperative population dynamics with concave nonlinearities

Martin Strugarek·Hongjun Ji
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Abstract

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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Martin Strugarek, Hongjun Ji. 2018-04-20. Sharp seasonal threshold property for cooperative population dynamics with concave nonlinearities. https://arxiv.org/abs/1804.07641

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