Sharp seasonal threshold property for cooperative population dynamics with concave nonlinearities

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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https://hal.archives-ouvertes.fr/hal-01772628
Contributor : Martin Strugarek <>
Submitted on : Friday, April 20, 2018 - 3:40:00 PM
Last modification on : Tuesday, December 10, 2019 - 3:08:21 PM
Long-term archiving on: Tuesday, September 18, 2018 - 6:47:30 PM

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  • HAL Id : hal-01772628, version 1
  • ARXIV : 1804.07641

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Martin Strugarek, Hongjun Ji. Sharp seasonal threshold property for cooperative population dynamics with concave nonlinearities. 2018. ⟨hal-01772628⟩

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